A method for calculating the maximum openable capacity of a multi-node active distribution network considering multi-user access

Abstract

The present application relates to a kind of active distribution network multi-node maximum openable capacity calculation method considering multiple user access, comprising the following steps: using Newton-Raphson method to carry out power flow calculation to active distribution network;Multiple user access is considered to the active distribution network multi-node maximum openable capacity calculation model;Using NSGA-Ⅱ to solve the active distribution network multi-node maximum openable capacity calculation model considering multiple user access, obtains the active distribution network multi-node maximum openable capacity considering multiple user access.This method can effectively deal with the condition that multiple users such as distributed power supply, load simultaneously access multiple nodes of active distribution network, can accurately calculate the maximum openable capacity of multiple nodes, and can provide the feasible region of the maximum openable capacity of multiple nodes, can provide important reference value for the planning and operation of active distribution network.

Description

Technical Field

[0001] This relates to the field of power systems, and in particular to a method for calculating the maximum open capacity of multiple nodes in an active distribution network that takes into account the access of multiple users. Background Technology

[0002] With the growing prominence of the energy crisis, renewable energy generation is of great significance in solving the problem. However, the increasing penetration rate of renewable energy generation will bring problems such as voltage fluctuations, bidirectional power flow, and complex operation and control to traditional distribution networks. Against this backdrop, active distribution networks have emerged. Active distribution networks have proactive control capabilities, enabling the scheduling of various units to ensure the reliable and stable operation of the distribution network.

[0003] Active distribution networks emphasize "active," meaning that the distribution network can coordinate the supply and load sides by regulating its components, such as distributed generation and controllable loads, enabling reliable and flexible operation. The maximum open capacity of an active distribution network is defined as the maximum capacity of loads and distributed generation that can be connected while satisfying power flow equations and operational safety conditions. Open capacity assessment is one of the main tools for active distribution network planning and operation, providing significant reference value for improving network reliability and developing upgrade and transformation strategies. Traditional methods for assessing open capacity in active distribution networks involve increasing loads based on a specified topology until equipment limits are reached. These methods rely primarily on manual judgment and empirical formulas, which can lead to low efficiency in business expansion applications, unscientific load allocation, and, to some extent, overloading and over-congestion of active distribution network equipment.

[0004] However, existing research on the available capacity assessment methods for active distribution networks only evaluates the available capacity of loads or feeders, failing to consider the situation where multiple users, such as distributed generation sources and loads, simultaneously connect to multiple nodes. In reality, when multiple users are connected, the power flow of an active distribution network changes significantly compared to when only a single type of user is connected. Using traditional available capacity assessment methods for single-type user connections would result in substantial errors. Therefore, there is an urgent need to develop a method for calculating the maximum available capacity of multiple nodes in an active distribution network that considers the connection of multiple users. Summary of the Invention

[0005] The main technical problem to be solved is to provide a method for calculating the maximum open capacity of multiple nodes in an active distribution network that takes into account the access of multiple users.

[0006] The following technical solution is adopted:

[0007] Power flow calculations for active distribution networks are performed using the Newton-Raphson method.

[0008] A calculation model for the maximum open capacity of multiple nodes in an active distribution network considering diverse user access.

[0009] The NSGA-II model for calculating the maximum open capacity of multiple nodes in an active distribution network considering multiple user access is solved to obtain the maximum open capacity of multiple nodes in an active distribution network considering multiple user access.

[0010] Specifically, the steps include:

[0011] The Newton-Raphson method is used to perform power flow calculations on active distribution networks, including:

[0012] The maximum open capacity of an active distribution network is defined as the maximum capacity of loads and distributed generation sources that can be connected under the conditions of satisfying the power flow equations and operational safety. The power flow calculation method used is the Newton-Raphson method. The Newton-Raphson algorithm transforms the nonlinear equations into a locally linearized system through multiple iterations, ultimately obtaining an approximate solution close to the true value within an effective accuracy range. The power flow equations using the nodal voltage method have two coordinate representations; here, rectangular coordinates are used. The rectangular coordinate power flow equation expression is obtained as follows:

[0013]

[0014]

[0015] In the formula, P i and Q i It refers to the active and reactive power of node i in the active distribution network; e i and f i These are the real and imaginary parts of the voltage at node i, respectively; G ij and B ij These are the conductance and susceptance of line ij, respectively; n is the number of nodes in the active distribution network.

[0016] For a system with n nodes, assuming that nodes 1, 2, ..., m are PQ nodes, and the active power and reactive power corresponding to the i-th PQ node are Pi and Pi, respectively. is Q is The equations for each PQ node can be written as follows:

[0017]

[0018] In the formula, △P i and △Q i These represent the active power deviation and reactive power deviation of node i, respectively.

[0019] The (m+1)th, (m+2)th, ..., (n-1)th nodes in the system are designated as PV nodes, and the nth node is designated as the slack node, with its voltage U n=e n +jf n It is known and does not participate in power flow calculation. Let the active power of the i-th PV node be P. is The given voltage is U is The power flow formula for this type of node is:

[0020]

[0021] In the formula, △U i Let be the voltage deviation at node i.

[0022] Represented as a block matrix:

[0023]

[0024] In the formula, H, N, M, L, R, and S are Jacobi matrix elements in the block matrix.

[0025] The expressions for each element of the Jacobian matrix in the block matrix are as follows:

[0026]

[0027]

[0028]

[0029]

[0030]

[0031]

[0032] Before performing power flow calculations using the Newton-Raphson method, the power network structure must be analyzed. The nodal admittance matrices are written based on the lines and power components. The relevant nodal inputs are determined according to the nodal types, and iterative calculations are performed until convergence is met. The basic steps of power flow calculation using the Newton-Raphson method are as follows:

[0033] 1) Form the nodal admittance matrix.

[0034] 2) Set the real part of the node voltage in rectangular coordinate form as The imaginary part is In the first iteration, k = 0.

[0035] 3) The node voltage value calculated based on the k-th iteration and Calculate the imbalance of each type of node. and

[0036] 4) Calculate the elements of each Jacobian matrix.

[0037] 5) Solve the block matrix to obtain the correction amount Δe for the node voltage. (k) , △f (k) .

[0038] 6) Determine whether the power flow calculation has converged, i.e.

[0039] max{|△e (k) ,△f (k) |}<ε (12)

[0040] 7) If the convergence criterion is met, the iteration ends, the iteration count is derived, and the final power flow calculation result is output; if convergence fails, the iteration count is incremented by 1, and the process returns to step 3), while the voltage of each node is corrected as follows:

[0041]

[0042] A calculation model for the maximum open capacity of multiple nodes in an active distribution network considering diverse user access includes...

[0043] Suppose that N diverse users simultaneously connect to N nodes in an active distribution network, including loads and distributed generation sources. Then the proposed model contains N objective functions:

[0044]

[0045] In the formula, f i Let be the objective function of the multi-user maximum open capacity calculation model for the i-th node of an active distribution network; and These represent the maximum available load capacity of the i-th node in the active distribution network and the maximum available capacity of distributed generation, respectively. and These are binary auxiliary variables representing the maximum open capacity of the load at the i-th node of the active distribution network and the maximum open capacity of distributed generation, respectively.

[0046] The proposed model is constrained by power flow equations, node voltages, and thermal stability. The power flow equation constraints for an active distribution network are shown below:

[0047]

[0048] In the formula, P i and Q i These represent the active power and reactive power of node i, respectively; G ij and B ij These are the conductance and susceptance of branch ij, respectively; e i and fi These are the real and imaginary parts of the voltage at node i, respectively.

[0049] The node voltage constraints of an active distribution network are shown below:

[0050]

[0051] In the formula, U i Let be the voltage value at node i; and These are the upper and lower voltage limits for node i, respectively.

[0052] The thermal stability constraints of the active distribution network are as follows:

[0053]

[0054] In the formula, S ij The apparent power of branch ij reflects the thermal stability of the branch. and These are the upper and lower limits of the apparent power of branch ij, respectively.

[0055] The NSGA-II model for calculating the maximum open capacity of multiple nodes in an active distribution network considering multiple user access is solved to obtain the maximum open capacity of multiple nodes in an active distribution network considering multiple user access, including:

[0056] The proposed model for calculating the maximum open capacity of multiple nodes in an active distribution network considering multiple user access has N objective functions and includes nonlinear power flow equation constraints, making it difficult to solve directly using commercial solvers. NSGA-II improves upon the traditional genetic algorithm by introducing an elitist strategy, a congestion estimation strategy, and a fast non-dominated sorting strategy, effectively solving the multi-objective nonlinear optimization model. Therefore, using NSGA-II to solve the proposed model for calculating the maximum open capacity of multiple nodes in an active distribution network can yield the maximum open capacity of multiple nodes in an active distribution network considering multiple user access.

[0057] The beneficial effects are:

[0058] A model for calculating the maximum open capacity of multiple nodes in an active distribution network considering the simultaneous access of multiple users is proposed. Solving the proposed model using NSGA-II yields the feasible region of the maximum open capacity when multiple nodes in the active distribution network are simultaneously connected to multiple users. The proposed model effectively addresses the scenario where distributed generation, loads, and other multiple users are simultaneously connected to multiple nodes in an active distribution network. It accurately calculates the maximum open capacity of multiple nodes and provides the feasible region of the maximum open capacity for multiple nodes, offering significant reference value for the planning and operation of active distribution networks. Attached Figure Description

[0059] Figure 1 This is a schematic diagram of the overall process.

[0060] Figure 2 This is a diagram of the IEEE 33-node distribution network structure.

[0061] Figure 3 This represents the maximum openable capacity feasible region for nodes 17 and 18.

[0062] Figure 4 The maximum openable capacity feasible region for nodes 2, 25, and 33. Detailed Implementation

[0063] The accompanying drawings are for illustrative purposes only and should not be construed as limiting this patent; it is understandable that some well-known structures and their descriptions may be omitted in the drawings for those skilled in the art. The positional relationships described in the drawings are for illustrative purposes only and should not be construed as limiting this patent.

[0064] A method for calculating the maximum open capacity of multiple nodes in an active distribution network considering the access of multiple users is proposed. The implementation process includes the following detailed steps:

[0065] Step 1: Perform power flow calculations on the active distribution network using the Newton-Raphson method.

[0066] The maximum open capacity of an active distribution network is defined as the maximum capacity of loads and distributed generation sources that can be connected under the conditions of satisfying the power flow equations and operational safety. The power flow calculation method used is the Newton-Raphson method. The Newton-Raphson algorithm transforms the nonlinear equations into a locally linearized system through multiple iterations, ultimately obtaining an approximate solution close to the true value within an effective accuracy range. The power flow equations using the nodal voltage method have two coordinate representations; here, rectangular coordinates are used. The rectangular coordinate power flow equation expression is obtained as follows:

[0067]

[0068]

[0069] In the formula, P i and Q i It refers to the active and reactive power of node i in the active distribution network; e i and f i These are the real and imaginary parts of the voltage at node i, respectively; G ij and B ij These are the conductance and susceptance of line ij, respectively; n is the number of nodes in the active distribution network.

[0070] For a system with n nodes, assuming that nodes 1, 2, ..., m are PQ nodes, and the active power and reactive power corresponding to the i-th PQ node are Pi and Pi, respectively. is Q is The equations for each PQ node can be written as follows:

[0071]

[0072] In the formula, △P i and △Q i These represent the active power deviation and reactive power deviation of node i, respectively.

[0073] The (m+1)th, (m+2)th, ..., (n-1)th nodes in the system are designated as PV nodes, and the nth node is designated as the slack node, with its voltage U n =e n +jf n It is known and does not participate in power flow calculation. Let the active power of the i-th PV node be P. is The given voltage is U is The power flow formula for this type of node is:

[0074]

[0075] In the formula, △U i Let be the voltage deviation at node i.

[0076] Represented as a block matrix:

[0077]

[0078] In the formula, H, N, M, L, R, and S are Jacobi matrix elements in the block matrix.

[0079] The expressions for each element of the Jacobian matrix in the block matrix are as follows:

[0080]

[0081]

[0082]

[0083]

[0084]

[0085]

[0086] Before performing power flow calculations using the Newton-Raphson method, the power network structure must be analyzed. The nodal admittance matrices are written based on the lines and power components. The relevant nodal inputs are determined according to the nodal types, and iterative calculations are performed until convergence is met. The basic steps of power flow calculation using the Newton-Raphson method are as follows:

[0087] 1) Form the nodal admittance matrix.

[0088] 2) Set the real part of the node voltage in rectangular coordinate form as The imaginary part is In the first iteration, k = 0.

[0089] 3) The node voltage value calculated based on the k-th iteration and Calculate the imbalance of each type of node. and

[0090] 4) Calculate the elements of each Jacobian matrix.

[0091] 5) Solve the block matrix to obtain the correction amount Δe for the node voltage. (k) , △f (k) .

[0092] 6) Determine whether the power flow calculation has converged, i.e.

[0093] max{|△e (k) ,△f (k) |}<ε (27)

[0094] 7) If the convergence criterion is met, the iteration ends, the iteration count is derived, and the final power flow calculation result is output; if convergence fails, the iteration count is incremented by 1, and the process returns to step 3), while the voltage of each node is corrected as follows:

[0095]

[0096] Step 2: Calculate the maximum open capacity of multiple nodes in an active distribution network considering the access of multiple users.

[0097] Suppose that N diverse users simultaneously connect to N nodes in an active distribution network, including loads and distributed generation sources. Then the proposed model contains N objective functions:

[0098]

[0099] In the formula, f i Let be the objective function of the multi-user maximum open capacity calculation model for the i-th node of an active distribution network; and These represent the maximum available load capacity of the i-th node in the active distribution network and the maximum available capacity of distributed generation, respectively. and These are binary auxiliary variables representing the maximum open capacity of the load at the i-th node of the active distribution network and the maximum open capacity of distributed generation, respectively.

[0100] The proposed model is constrained by power flow equations, node voltages, and thermal stability. The power flow equation constraints for an active distribution network are shown below:

[0101]

[0102] In the formula, P i and Q i These represent the active power and reactive power of node i, respectively; G ij and B ij These are the conductance and susceptance of branch ij, respectively; e i and f i These are the real and imaginary parts of the voltage at node i, respectively.

[0103] The node voltage constraints of an active distribution network are shown below:

[0104]

[0105] In the formula, U i Let be the voltage value at node i; and These are the upper and lower voltage limits for node i, respectively.

[0106] The thermal stability constraints of the active distribution network are as follows:

[0107]

[0108] In the formula, S ij The apparent power of branch ij reflects the thermal stability of the branch. and These are the upper and lower limits of the apparent power of branch ij, respectively.

[0109] Step 3: Use NSGA-II to solve the calculation model of the maximum open capacity of multiple nodes in an active distribution network considering multiple user access, and obtain the maximum open capacity of multiple nodes in an active distribution network considering multiple user access.

[0110] The proposed model for calculating the maximum open capacity of multiple nodes in an active distribution network considering multiple user access has N objective functions and includes nonlinear power flow equation constraints, making it difficult to solve directly using commercial solvers. NSGA-II improves upon the traditional genetic algorithm by introducing an elitist strategy, a congestion estimation strategy, and a fast non-dominated sorting strategy, effectively solving the multi-objective nonlinear optimization model. Therefore, using NSGA-II to solve the proposed model for calculating the maximum open capacity of multiple nodes in an active distribution network can yield the maximum open capacity of multiple nodes in an active distribution network considering multiple user access.

[0111] To further understand, the following uses the IEEE-33 node active distribution network as an example to explain its practical application.

[0112] by Figure 2 The IEEE 33-node active distribution network shown is used as an example for analysis. In the figure, numbers 1 to 33 represent 33 nodes. The line parameters and node parameters of the system are shown in Table 1. Node 1 is set as the slack node with a base capacity of 10MVA and a base voltage of 12.66KV. U is taken as... min,k =0.95pu, U max,k =1.05 pu, the total network load is 3.715 + 2.3 iMVA. Following the steps above, the maximum open capacity is calculated.

[0113] First, the proposed model was used to calculate the maximum available capacity of each node in the active distribution network under the condition of user access to a single node. The results are shown in Table 1. Table 1 shows that the maximum available load capacity and the maximum available distributed generation capacity of node 2 are the highest among all nodes except the slack node. Furthermore, the maximum available load capacity and the maximum available distributed generation capacity of nodes farther from the slack node generally show a gradually decreasing trend. For example, nodes 19-25, which are closer to the slack node, have average maximum available load capacity and maximum available distributed generation capacity of 51.7MW and 108.2MW, respectively, while nodes 12-18, which are farther from the slack node, have average maximum available load capacity and maximum available distributed generation capacity of only 30.4MW and 106.0MW, respectively.

[0114] Table 1. Available load capacity and available distributed generation capacity at each node in the IEEE 33-node power distribution system.

[0115]

[0116]

[0117] Next, we calculate the maximum available capacity of the two nodes for the case where two users simultaneously connect to two different nodes in the active distribution network. Taking nodes 17 and 18 as examples, the feasible region of the maximum available capacity of these two nodes is as follows: Figure 3 As shown. In Figure 3 In the diagram, the first quadrant indicates that both nodes 17 and 18 are connected to load users; the second quadrant indicates that node 17 is connected to a distributed power source user, and node 18 is connected to a load user; the third quadrant indicates that both nodes 17 and 18 are connected to distributed power source users; and the fourth quadrant indicates that node 17 is connected to a load user, and node 18 is connected to a distributed power source user. Figure 3 It can be seen that when nodes 17 and 18 are simultaneously connected to load users, their maximum available load capacity exhibits a "one-to-one" relationship. Referring to Table 1, the horizontal and vertical intercepts of the feasible region in the first quadrant represent the maximum available load capacity of a single node for nodes 17 and 18, respectively, as shown in Table 1. When nodes 17 and 18 are simultaneously connected to distributed generation users, their maximum available distributed generation capacity is similar to that in the first quadrant. The horizontal and vertical intercepts of the feasible region in the second quadrant represent the maximum available distributed generation capacity of a single node for nodes 17 and 18, respectively, as shown in Table 1. When node 17 is connected to a distributed generation user and node 18 is connected to a load user, the maximum available load capacity of node 18 increases from 24.3MW in Table 1 to 93.5MW. This is because after node 17 is connected to a distributed generation user, node 18 is supplied not only by the balancing node but also by node 17, thus significantly increasing its maximum available load capacity.

[0118] Similarly, we calculate the maximum available capacity of the three nodes when three users simultaneously connect to three different nodes in an active distribution network. Taking nodes 2, 25, and 33 as examples, the feasible region of the maximum available capacity of these three nodes is as follows: Figure 4As shown, the feasible region of the maximum open capacity for 3 nodes is a three-dimensional graph. The first quadrant represents all three nodes connected to load users; the second quadrant represents node 2 connected to distributed generation users, and nodes 25 and 33 connected to load users; the third quadrant represents nodes 2 and 25 connected to distributed generation users, and node 33 connected to load users; the fourth quadrant represents node 33 connected to distributed generation users, and nodes 2 and 33 connected to load users; the fifth quadrant represents nodes 2 and 25 connected to load users, and node 33 connected to distributed generation users; the sixth quadrant represents nodes 2 and 33 connected to distributed generation users, and node 25 connected to load users; the seventh quadrant represents all three nodes connected to distributed generation users; and the eighth quadrant represents nodes 25 and 33 connected to distributed generation users, and node 2 connected to load users. Similarly, if 4 users are simultaneously connected to the active distribution network, the feasible region of open capacity is a four-dimensional graph; if 5 users are simultaneously connected to the active distribution network, it is a five-dimensional graph. Therefore, the proposed calculation model for the maximum open capacity of multiple nodes in an active distribution network can effectively address the situation where multiple users simultaneously access multiple nodes in an active distribution network, and can accurately calculate the feasible region of the maximum open capacity of multiple nodes.

Claims

1. A method for calculating the maximum openable capacity of multiple nodes in an active distribution network considering multiple user accesses, characterized in that, Including the following steps: Power flow calculations for active distribution networks are performed using the Newton-Raphson method. A calculation model for the maximum open capacity of multiple nodes in an active distribution network considering diverse user access. The maximum open capacity of multiple nodes in an active distribution network considering multiple user access is calculated using NSGA-II. A calculation model for the maximum open capacity of multiple nodes in an active distribution network considering diverse user access includes: Suppose that N diverse users simultaneously connect to N nodes in an active distribution network, and these diverse users include loads and distributed generation sources; then the proposed model contains N objective functions: In the formula, F i Let be the objective function of the multi-user maximum open capacity calculation model for the i-th node of an active distribution network; and These represent the maximum available load capacity of the i-th node in the active distribution network and the maximum available capacity of distributed generation, respectively. and These are binary auxiliary variables representing the maximum open capacity of the load at the i-th node of the active distribution network and the maximum open capacity of the distributed generation, respectively. The constraints of the model are power flow equation constraints, node voltage constraints, and thermal stability constraints.

2. The method for calculating the maximum openable capacity of multiple nodes in an active distribution network considering multiple user access as described in claim 1, characterized in that, The Newton-Raphson method is used to perform power flow calculations on active distribution networks, including: The maximum open capacity of an active distribution network is defined as the maximum capacity of loads and distributed generation sources that can be connected under the conditions of satisfying the power flow equations and operational safety. The power flow calculation method used is the Newton-Raphson method. The Newton-Raphson algorithm transforms the nonlinear equations into a locally linearized system through multiple iterations, ultimately obtaining an approximate solution close to the true value within an effective accuracy range. The power flow equations are written using the nodal voltage method, and there are two coordinate representations. Here, rectangular coordinates are used. The rectangular coordinate power flow equation expression is obtained as follows: ； ； In the formula, P i and Q i It refers to the active and reactive power of node i in the active distribution network; e i and f i These are the real and imaginary parts of the voltage at node i, respectively; G ij and B ij These are the conductance and susceptance of line ij, respectively; n is the number of nodes in the active distribution network. For a system with n nodes, assuming that nodes 1, 2, ..., m are PQ nodes, and the active power and reactive power corresponding to the i-th PQ node are Pi and Pi, respectively. is Q is The equations for each PQ node can be written as follows: ； In the formula, ΔP i and ΔQ i These are the active power deviation and reactive power deviation of node i, respectively; The (m+1)th, (m+2)th, ..., (n-1)th nodes in the system are designated as PV nodes, and the nth node is designated as the balancing node, whose voltage... It is known and does not participate in power flow calculation; let the active power of the i-th PV node be determined as follows. The given voltage is The power flow formula for this type of node is: ； In the formula, The voltage deviation at node i; Represented as a block matrix: ； In the formula, H, N, M, L, R, and S are Jacobi matrix elements in the block matrix; The expressions for each element of the Jacobian matrix in the block matrix are as follows: ； ； ； ； ； ； Before performing power flow calculations using the Newton-Raphson method, the power network structure must be analyzed. The node admittance matrices should be written based on the lines and power components. Relevant node inputs should be determined according to the node type, and iterative calculations should be performed until convergence is met. The basic steps of power flow calculation using the Newton-Raphson method are as follows: 1) Form the nodal admittance matrix; 2) Set the real part of the node voltage in rectangular coordinate form as The imaginary part is In the first iteration, k=0; 3) The node voltage value calculated based on the k-th iteration and Calculate the imbalance of each type of node. , and ; 4) Calculate the elements of each Jacobian matrix; 5) Solve the block matrix to obtain the correction amount of the node voltage. , ; 6) Determine whether the power flow calculation has converged, i.e. ； 7) If the convergence criterion is met, the iteration ends, the iteration count is derived, and the final power flow calculation result is output; if convergence fails, the iteration count is incremented by 1, and the process returns to step 3), while the voltage of each node is corrected as follows; 。 3. The method for calculating the maximum openable capacity of multiple nodes in an active distribution network considering multiple user access as described in claim 1, characterized in that, The power flow equation constraints for an active distribution network are shown below: ； In the formula, and These are the active power and reactive power of node i, respectively; and These are the conductance and susceptance of branch ij, respectively; i and f i These are the real and imaginary parts of the voltage at node i, respectively; The node voltage constraints of an active distribution network are shown below: ； In the formula, Let be the voltage value at node i; and These are the upper and lower voltage limits for node i, respectively; The thermal stability constraints of the active distribution network are as follows: ； In the formula, The apparent power of branch ij reflects the thermal stability of the branch. and These are the upper and lower limits of the apparent power of branch ij, respectively.

4. The method for calculating the maximum openable capacity of multiple nodes in an active distribution network considering multiple user access, as described in claim 1, is characterized in that... The NSGA-II model for calculating the maximum open capacity of multiple nodes in an active distribution network considering multiple user access is solved to obtain the maximum open capacity of multiple nodes in an active distribution network considering multiple user access, including: The calculation model for the maximum open capacity of multiple nodes in an active distribution network considering multiple user access has N objective functions and includes nonlinear power flow equation constraints, making it difficult to solve directly using commercial solvers. NSGA-II improves the traditional genetic algorithm by introducing an elite strategy, a congestion estimation strategy, and a fast non-dominated sorting strategy, which can effectively solve the multi-objective nonlinear optimization model. Therefore, by using NSGA-II to solve the proposed calculation model for the maximum open capacity of multiple nodes in an active distribution network, the maximum open capacity of multiple nodes in an active distribution network considering multiple user access can be obtained.

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