A power distribution network stochastic power flow acceleration algorithm based on inter-area scene equivalence

Abstract

The application is a power distribution network random power flow acceleration algorithm based on inter-regional scene equivalence, relates to the field of random power flow algorithm, and comprises the following steps: a multi-regional power flow model that influences each other through boundary quantity is established, an inter-regional scene equivalence method is proposed, and a distributed solution algorithm of random power flow is designed. The application considers the problem that a huge calculation burden is caused by a large number of simulations on node injection power in the random power flow algorithm, constructs a multi-regional power flow model that influences each other through boundary quantity, proposes an inter-regional scene equivalence method, and reduces redundant scene information in the information transmission process. Further, a distributed solution algorithm of random power flow is designed on the basis, reduces the scene number of the traditional centralized type in an exponential form, can solve more scenes under the same time constraint, and avoids the problem of too large operation quantity.

Description

Technical Field

[0001] This invention relates to the field of stochastic power flow algorithms, specifically a stochastic power flow acceleration algorithm for distribution networks based on inter-regional scenario equivalence. Background Technology

[0002] Driven by the "dual-carbon" strategic goal, the penetration rate of distributed photovoltaic (PV) power in distribution networks is continuously increasing. The large-scale deployment of distributed PV, characterized by "small capacity and large number," to the user side has led to significant changes in power flow distribution due to the uncertainty and intermittency of its output, making the stochastic challenges facing distribution networks increasingly prominent. Stochastic power flow, as a crucial tool for quantitatively analyzing the impact of uncertainties on the operating state of distribution systems, can effectively handle uncertainties in system operation and obtain the probability distribution of system state variables. However, distribution network stochastic power flow algorithms require extensive simulations of power injection at each node. The large-scale deployment of distributed PV, characterized by "small capacity and large number," to the user side introduces redundant scenario information during information transmission, while the exponentially increasing number of scenarios in traditional centralized systems results in a huge computational burden, leading to low computational efficiency. Summary of the Invention

[0003] The technical problem to be solved by this invention is to overcome the disadvantage of low computational efficiency caused by simulating a large amount of power injection into nodes, and to provide a distribution network stochastic power flow acceleration algorithm based on inter-regional scenario equivalence.

[0004] The solution to the technical problem of this invention is: a distribution network stochastic power flow acceleration algorithm based on inter-regional scenario equivalence, characterized by the following steps:

[0005] 1) Establish a multi-region power flow model where each region interacts through boundary quantities;

[0006] 2) A method for equivalence of scenes between regions is proposed;

[0007] ① An equivalent method for the main region in sub-regions with different power injection scenarios;

[0008] ② Equivalence method for sub-regions with different power injection scenarios within the main region;

[0009] 3) Design an accelerated algorithm for distributed solution of stochastic power flow in distribution networks;

[0010] ① Solving stochastic power flow in the main region;

[0011] ② Solving for stochastic power flow in subregions.

[0012] Furthermore, step 1) involves a multi-region power flow model where boundary quantities interact, including establishing a distribution network power flow model, a power flow model for a multi-region topology, a power flow model for the backbone region, and power flow models for sub-regions, as detailed below:

[0013] ① The power flow model of the distribution network adopts the Distflow model, and the expression is shown in formula (1):

[0014] (1)

[0015] In formula (1), the subscript of the variable i and j For the node number of the distribution network; for the subscript of the variable. ij Line number; P ij For the line ij Active power at the beginning; Q ij For the line ij Initial reactive power; I ij For the line ij The current flowing through it; P jh and Q jh For the line jh Initial active and reactive power; v i and v j For nodes i and nodes j The magnitude of the voltage; P j 、Q j These represent the active power and reactive power injected into the node, respectively. H j For the node j The set of downstream nodes connected to it; r ij and x ij These are the resistance and reactance of the circuit, respectively.

[0016] ②The power flow model for a multi-region topology is shown in formula (2):

[0017] (2)

[0018] In formula (2), U n Indicates the first n The node voltage matrix within each region; For vectors U0, , , U n The transpose of the resulting matrix; U 0 The node voltage matrix of the main region; U n Let n be the node voltage matrix of subregion n; and The first node and the second node in the main region, respectively. The injected power of each node; and The sub-sub ... The injected power of each node; The number of all nodes within subregion n; The number of all nodes within the main region; F U The relationship between the injected power at each node and the voltage at each node is a function of the power flow model.

[0019] ③ The power flow model of the main region is the power injected into the boundaries of each sub-region. Power injection in the main region The function is shown in formula (3):

[0020] (3)

[0021] In the formula, and These are the boundary injection powers for sub-region 1 and sub-region n, respectively.

[0022] ④ The power flow model within a sub-region is its boundary voltage. U n.B and internal injected power The power flow model of the function can be represented by a set of equations (4):

[0023] (4)

[0024] In the formula, U n.B Subregion n The boundary voltage.

[0025] Furthermore, the inter-regional scene equivalence method described in step 2) involves equivalence of scenarios where power injection within a region has the same impact on the boundary quantities of other regions, resulting in the following scene equivalence method:

[0026] Sub-region scene equivalence method: While keeping the injected power in the main region unchanged, sub-regions... nAll injection scenarios are incorporated into the power flow model (1) of the distribution network to obtain sub-regions. n The boundary injection power matrix under different scenarios is shown in Equation (5):

[0027] (5)

[0028] In the formula, The number of scenarios in which power is injected into the boundary of sub-region n;

[0029] In formula (5), if there are two scene pairs of sub-regions n If the boundary injection power satisfies equation (6), then the two scenarios are considered equivalent:

[0030] (6)

[0031] In the formula, for Sub-regions in the scene n Boundary injection power; Inject scene differences into the boundary power within the sub-region;

[0032] Scene equivalence method for the main region: in sub-regions n Under the condition that the internal node injected power remains unchanged, all power injection scenarios in the main area are brought into the power flow model of the distribution network (1) to obtain the sub-region. n The boundary voltage matrix is ​​shown in equation (7):

[0033] (7)

[0034] In the formula, sub-region n The number of scenarios involving boundary voltages;

[0035] In formula (7), if there are two scene pairs of sub-regions n If the boundary voltage satisfies equation (8), then the two scenarios are equivalent:

[0036] (8)

[0037] In the formula, for Sub-regions in the scene n Boundary voltage; Power injection scenarios between sub-regions within the main region n The difference in the effect of boundary voltage.

[0038] Furthermore, the accelerated algorithm for distributed solution of distribution network stochastic power flow in step 3) is to reconstruct the power flow model based on the stochastic power injection information within the region and the equivalent scenario information exchanged between regions, thereby achieving accelerated solution of stochastic power flow, as detailed below:

[0039] ① Solving stochastic power flow in the main region

[0040] Sub-region a transfers the equivalent boundary injection power to the backbone region based on the inter-region scene equivalence method described in step 2).

[0041] b. By replacing the node injection power within each sub-region of the distribution network power flow model (1) with their respective boundary injection power, a new distribution network power flow model can be constructed within the main region. The first two equations of the distribution network power flow model (1) are replaced with equation (9), while the last two equations remain unchanged:

[0042] (9)

[0043] In the formula, H j0 Nodes within the main trunk area j The set of downstream nodes connected to it; P in.0n Main region to sub-region n Active power injected at the boundary; Q in.0n Main region to sub-region n Reactive power is injected at the boundary; L j For nodes j The set of sub-region numbers connected to it downstream;

[0044] c. Based on the power flow model of the distribution network constructed in step b, the boundary injection power information transferred by each sub-region and the random power injection information inside itself are used to form a set of power injection scenarios in the main region. This scenario is then substituted into formula (9) and solved using the Newton iteration method. The result of the distributed solution of the random power flow of the distribution network in the main region can be obtained.

[0045] ② Solving the random power flow in the subregion

[0046] When the injected power in the main region and other sub-regions is determined, the boundary voltage in formula (4) will be used. U n.B In sub-region n The internal power injection points are subjected to a first-order Taylor expansion, as shown in Equation (10).

[0047] (10)

[0048] In the formula, sub-region n The reference value of the boundary voltage after the first-order Taylor expansion; These are the coefficients of the first-order Taylor expansion; It is a sub-region n Inner k The change in injected power at each node;

[0049] After processing in step a, the boundary voltage of the sub-region can be divided into two parts: the baseline value caused by power injection at each node of the distribution network and the change value caused by power injection within the sub-region.

[0050] c. Introduce the sensitivity of each node's power injection to its boundary voltage within the sub-region, and substitute it into formula (10) to obtain the boundary voltage under different power injections in the sub-region;

[0051] Using the boundary voltage as the root node, the power flow equations are reconstructed under the topology of the subregion, and the stochastic power flow calculation results of the subregion are obtained by solving the equations using the Newton-Raphson iteration method.

[0052] The beneficial effects of this invention are as follows: Addressing the problem of low computational efficiency caused by the need for extensive simulation of power injection at each node in distribution network stochastic power flow algorithms, this invention constructs a multi-regional power flow model that interacts through boundary quantities. It proposes an accelerated distribution network stochastic power flow algorithm based on inter-regional scenario equivalence, reducing redundant scenario information during information transmission, decreasing the exponentially increasing number of scenarios in traditional centralized algorithms, and enabling the solution of more scenarios under the same time constraints. This avoids excessive computational load and thus improves solution efficiency. Attached Figure Description

[0053] Figure 1 This is a schematic diagram of the multi-regional power distribution network structure of the present invention;

[0054] Figure 2 A schematic diagram illustrating the equivalent scenario of injecting power into a sub-region on the main region.

[0055] Figure 3 Main region to sub-region n A scene equivalent diagram;

[0056] Figure 4 This is a flowchart of the distributed computing process for random power flow in this invention;

[0057] Figure 5 This is a topology diagram of the IEEE 118 example system;

[0058] Figure 6 A scatter plot showing the power output of each photovoltaic power station;

[0059] Figure 7Inject a scatter plot of the boundary power of sub-region 1;

[0060] Figure 8 The boundary quantity diagram of sub-region 2 under the power injection of the main region;

[0061] Figure 9 A diagram showing the relative error of voltage and power at all nodes in the main trunk region;

[0062] Figure 10 A graph showing the relative error of voltage and power at all nodes in sub-region 1;

[0063] Figure 11 This is a graph showing the relative error between voltage and power at all nodes in sub-region 2. Detailed Implementation

[0064] The present invention will be further described below with reference to the accompanying drawings and examples.

[0065] See Figure 1-4 This embodiment presents a distribution network stochastic power flow acceleration algorithm based on inter-regional scenario equivalence, comprising the following steps:

[0066] 1) Establish a multi-region power flow model where each region interacts through boundary quantities;

[0067] 2) A method for equivalence of scenes between regions is proposed;

[0068] ① An equivalent method for the main region in sub-regions with different power injection scenarios;

[0069] ② Equivalence method for sub-regions with different power injection scenarios within the main region;

[0070] 3) Design an accelerated algorithm for distributed solution of stochastic power flow in distribution networks;

[0071] ① Solving stochastic power flow in the main region;

[0072] ② Solving for stochastic power flow in subregions.

[0073] Furthermore, step 1) involves a multi-region power flow model where boundary quantities interact, including establishing a distribution network power flow model, a power flow model for a multi-region topology, a power flow model for the backbone region, and power flow models for sub-regions, as detailed below:

[0074] ① The power flow model of the distribution network adopts the Distflow model, and the expression is shown in formula (1):

[0075] (1)

[0076] In formula (1), the subscript of the variable i and j For the node number of the distribution network; for the subscript of the variable. ij Line number; P ij For the line ij Active power at the beginning; Q ij For the line ij Initial reactive power; I ij For the line ij The current flowing through it; P jh and Q jh For the line jh Initial active and reactive power; v i and v j For nodes i and nodes j The magnitude of the voltage; P j 、Q j These represent the active power and reactive power injected into the node, respectively. H j For the node j The set of downstream nodes connected to it; r ij and x ij These are the resistance and reactance of the circuit, respectively.

[0077] ②The power flow model for a multi-region topology is shown in formula (2):

[0078] (2)

[0079] In formula (2), U n Indicates the first n The node voltage matrix within each region; For vectors U 0, , , U n The transpose of the resulting matrix; U 0 The node voltage matrix of the main region; U n Let n be the node voltage matrix of subregion n; and The first node and the second node in the main region, respectively. The injected power of each node; and The sub-sub ... The injected power of each node; The number of all nodes within subregion n; The number of all nodes within the main region; F U The relationship between the injected power at each node and the voltage at each node is a function of the power flow model.

[0080] ③ The power flow model of the main region is the power injected into the boundaries of each sub-region. Power injection in the main region The function is shown in formula (3):

[0081] (3)

[0082] In the formula, and These are the boundary injection powers for sub-region 1 and sub-region n, respectively.

[0083] ④ The power flow model within a sub-region is its boundary voltage. U n.B and internal injected power The power flow model of the function can be represented by a set of equations (4):

[0084] (4)

[0085] In the formula, U n.B Subregion n The boundary voltage.

[0086] Furthermore, the inter-regional scene equivalence method described in step 2) involves equivalence of scenarios where power injection within a region has the same impact on the boundary quantities of other regions, resulting in the following scene equivalence method:

[0087] ① Sub-region scene equivalence method: While keeping the injected power in the main region unchanged, the sub-region scene equivalence method is used. n All injection scenarios are incorporated into the power flow model (1) of the distribution network to obtain sub-regions. n The boundary injection power matrix under different scenarios is shown in Equation (5):

[0088] (5)

[0089] In the formula, The number of scenarios in which power is injected into the boundary of sub-region n;

[0090] In formula (5), if there are two scene pairs of sub-regions n If the boundary injection power satisfies equation (6), then the two scenarios are considered equivalent:

[0091] (6)

[0092] In the formula, for Sub-regions in the scene n Boundary injection power; Inject scene differences into the boundary power within the sub-region;

[0093] ② Scene equivalence method for the main region: in the sub-region n Under the condition that the internal node injected power remains unchanged, all power injection scenarios in the main area are brought into the power flow model of the distribution network (1) to obtain the sub-region. n The boundary voltage matrix is ​​shown in equation (7):

[0094] (7)

[0095] In the formula, sub-region n The number of scenarios involving boundary voltages;

[0096] In formula (7), if there are two scene pairs of sub-regions n If the boundary voltage satisfies equation (8), then the two scenarios are equivalent:

[0097] (8)

[0098] In the formula, for Sub-regions in the scene n Boundary voltage; Power injection scenarios between sub-regions within the main region n The difference in the effect of boundary voltage.

[0099] Furthermore, the accelerated algorithm for distributed solution of distribution network stochastic power flow in step 3) is to reconstruct the power flow model based on the stochastic power injection information within the region and the equivalent scenario information exchanged between regions, thereby achieving accelerated solution of stochastic power flow, as detailed below:

[0100] ① Solving stochastic power flow in the main region

[0101] Sub-region a transfers the equivalent boundary injection power to the backbone region based on the inter-region scene equivalence method described in step 2).

[0102] b. By replacing the node injection power within each sub-region of the distribution network power flow model (1) with their respective boundary injection power, a new distribution network power flow model can be constructed within the main region. The first two equations of the distribution network power flow model (1) are replaced with equation (9), while the last two equations remain unchanged:

[0103] (9)

[0104] In the formula, H j0 Nodes within the main trunk area j The set of downstream nodes connected to it; P in.0n Main region to sub-region n Active power injected at the boundary; Q in.0n Main region to sub-region n Reactive power is injected at the boundary; L j For nodes j The set of sub-region numbers connected to it downstream;

[0105] c. Based on the power flow model of the distribution network constructed in step b, the boundary injection power information transferred by each sub-region and the random power injection information inside itself are used to form a set of power injection scenarios in the main region. This scenario is then substituted into formula (9) and solved using the Newton iteration method. The result of the distributed solution of the random power flow of the distribution network in the main region can be obtained.

[0106] ② Solving the random power flow in the subregion

[0107] When the injected power in the main region and other sub-regions is determined, the boundary voltage in formula (4) will be used. U n.B In sub-region n The internal power injection points are subjected to a first-order Taylor expansion, as shown in Equation (10).

[0108] (10)

[0109] In the formula, sub-region n The reference value of the boundary voltage after the first-order Taylor expansion; These are the coefficients of the first-order Taylor expansion; It is a sub-region n Inner k The change in injected power at each node;

[0110] After processing in step a, the boundary voltage of the sub-region can be divided into two parts: the baseline value caused by power injection at each node of the distribution network and the change value caused by power injection within the sub-region.

[0111] c. Introduce the sensitivity of each node's power injection to its boundary voltage within the sub-region, and substitute it into formula (10) to obtain the boundary voltage under different power injections in the sub-region;

[0112] Using the boundary voltage as the root node, the power flow equations are reconstructed under the topology of the subregion, and the stochastic power flow calculation results of the subregion are obtained by solving the equations using the Newton-Raphson iteration method.

[0113] Example 2, see Figure 5 As shown, this embodiment divides the distribution network into one main area and two sub-areas. The main area connects to 2MW of photovoltaic (PV) power at nodes 10, 64, 83, and 106; sub-area 1 connects to 3MW of PV power at nodes 28, 44, 50, and 51; and sub-area 2 connects to 2.5MW of PV power at nodes 69, 77, 94, and 98. Since the power factor of a PV power plant is typically above 0.95 during normal operation, this paper only considers the active power generated by the PV power plant, and the output active power is selected according to the maximum power point tracking (MPPT) principle. The sampling accuracy of Monte Carlo is the same as that of the method proposed in this paper.

[0114] The output of the 12 photovoltaic power stations set up above was obtained using a random sampling method, such as... Figure 6 As shown, each photovoltaic power station is characterized by three output scenarios, and it is assumed that the output of photovoltaic power stations is independent of each other.

[0115] With the power injection scenarios in the main region and sub-region 2 remaining unchanged, calculate and sort the boundary injection power under all photovoltaic power injection scenarios in sub-region 1.

[0116] Next, starting from the minimum boundary injection power, the values ​​are sequentially increased according to the power equality scenario differences, with the maximum boundary injection power used as the final cluster center. The final clustering result is as follows: Figure 7 As shown in the results, the 81 boundary power injection scenarios were clustered into 21 classes, effectively reducing the number of scenarios calculated. Assuming that the photovoltaic power injection scenarios in sub-region 1 and sub-region 2 remain unchanged, the square of the boundary voltage of sub-region 2 under all photovoltaic power injection scenarios in the main region is calculated and sorted.

[0117] Next, starting from the minimum value, the values ​​are sequentially increased according to the power equivalence scenario differences, and the largest squared boundary voltage (the boundary value of sub-region 2) is used as the final cluster center. The clustering results are as follows: Figure 8 As shown in the results, 81 boundary quantities were clustered into 7 classes, which effectively reduced the number of scenarios to be calculated.

[0118] Example 3, this example serves as a comparative example, based on Figure 6 All output scenarios of photovoltaic power plants, with 3 12 The results are based on 531,441 Monte Carlo simulations and are considered accurate.

[0119] The accuracy of the proposed distributed stochastic power flow algorithm is compared and analyzed when it is used in the main region, sub-region 1, and sub-region 2. Figure 9-11 The relative error statistics of node voltage and branch power in the main region, sub-region 1, and sub-region 2 are presented with respect to the Monte Carlo simulation method. This proves that the algorithm proposed in this invention is truly effective and can indeed reduce the number of scenarios that increase exponentially in the traditional centralized method. It can solve more scenarios under the same time constraints, thereby improving the solution efficiency.

[0120] The calculation conditions, illustrations, tables, etc. in the embodiments of this invention are only used to further illustrate the invention and are not exhaustive. They do not constitute a limitation on the scope of protection of the claims. Those skilled in the art, based on the inspiration gained from the embodiments of this invention, can conceive of other substantially equivalent alternatives without inventive effort, all of which are within the scope of protection of this invention.

Claims

1. A distribution network stochastic power flow acceleration algorithm based on inter-regional scenario equivalence, characterized by: Includes the following steps: 1) Establish a multi-region power flow model where each region interacts through boundary quantities; 2) A method for equivalence of scenes between regions is proposed; ① An equivalent method for the main region in sub-regions with different power injection scenarios; ② Equivalence method for sub-regions with different power injection scenarios within the main region; 3) Design an accelerated algorithm for distributed solution of stochastic power flow in distribution networks; ① Solving stochastic power flow in the main region; ② Solving for stochastic power flow in subregions; Step 1) involves establishing a multi-region power flow model that uses boundary quantities to influence each other. This includes building a distribution network power flow model, a power flow model for a multi-region topology, a power flow model for the backbone region, and power flow models for sub-regions, as detailed below: ① The power flow model of the distribution network adopts the Distflow model, and the expression is shown in formula (1): （1） In formula (1), the subscript of the variable i and j For the node number of the distribution network; for the subscript of the variable. ij Line number; P ij For the line ij Active power at the beginning; Q ij For the line ij Initial reactive power; I ij For the line ij The current flowing through it; P jh and Q jh For the line jh Initial active and reactive power; v i and v j For nodes i and nodes j The magnitude of the voltage; P j 、Q j These represent the active power and reactive power injected into the node, respectively. H j For the node j The set of downstream nodes connected to it; r ij and x ij These are the resistance and reactance of the circuit, respectively. ②The power flow model for a multi-region topology is shown in formula (2): （2） In formula (2), U n Indicates the first n The node voltage matrix within each region; For vectors U 0, , , U n The transpose of the resulting matrix; U 0 The node voltage matrix of the main region; U n Let n be the node voltage matrix of subregion n; and The first node and the second node in the main region, respectively. The injected power of each node; and The sub-sub ... The injected power of each node; The number of all nodes within subregion n; The number of all nodes within the main region; F U The relationship between the injected power at each node and the voltage at each node is a function of the power flow model. ③ The power flow model of the main region is the power injected into the boundaries of each sub-region. Power injection in the main region The function is shown in formula (3): （3） In the formula, and These are the boundary injection powers for sub-region 1 and sub-region n, respectively. ④ The power flow model within a sub-region is its boundary voltage. U n.B and internal injected power The function of the power flow model is represented by a set of equations (4): （4） In the formula, U n.B Subregion n Boundary voltage; Step 2) describes an inter-regional scene equivalence method that performs equivalence on scenes where power injection within a region has the same impact on the boundary quantities of other regions, resulting in the following scene equivalence method: Sub-region scene equivalence method: While keeping the injected power in the main region unchanged, sub-regions... n All injection scenarios are incorporated into the power flow model (1) of the distribution network to obtain sub-regions. n The boundary injection power matrix under different scenarios is shown in Equation (5): （5） In the formula, The number of scenarios in which power is injected into the boundary of sub-region n; In formula (5), if there are two scene pairs of sub-regions n If the boundary injection power satisfies equation (6), then the two scenarios are considered equivalent: （6） In the formula, for Sub-regions in the scene n Boundary injection power; Inject the difference between scenes into the boundary power within the sub-region; Scene equivalence method for the main region: in sub-regions n Under the condition that the internal node injected power remains unchanged, all power injection scenarios in the main area are brought into the power flow model of the distribution network (1) to obtain the sub-region. n The boundary voltage matrix is ​​shown in equation (7): （7） In the formula, sub-region n The number of scenarios involving boundary voltages; In formula (7), if there are two scene pairs of sub-regions n If the boundary voltage satisfies equation (8), then the two scenarios are equivalent: （8） In the formula, for Sub-regions in the scene n Boundary voltage; Power injection scenarios between sub-regions within the main region n The difference in the effect of boundary voltage; The accelerated algorithm for distributed solution of stochastic power flow in step 3) reconstructs the power flow model based on the stochastic power injection information within the region and the equivalent scenario information exchanged between regions, thereby achieving accelerated solution of stochastic power flow, as detailed below: ① Solving stochastic power flow in the main region Sub-region a transfers the equivalent boundary injection power to the backbone region based on the inter-region scene equivalence method described in step 2). b. By replacing the node injection power within each sub-region of the distribution network power flow model (1) with their respective boundary injection power, a new distribution network power flow model can be constructed within the main region. The first two equations of the distribution network power flow model (1) are replaced with equation (9), while the last two equations remain unchanged: （9） In the formula, H j0 Nodes within the main trunk area j The set of downstream nodes connected to it; P in.0n Main region to sub-region n Active power injected at the boundary; Q in.0n Main region to sub-region n Reactive power is injected at the boundary; L j For nodes j The set of sub-region numbers connected to it downstream; c. Based on the power flow model of the distribution network constructed in step b, the boundary injection power information transferred by each sub-region and the random power injection information inside itself are used to form a set of power injection scenarios in the main region. This scenario is then substituted into formula (9) and solved using the Newton iteration method. The result of the distributed solution of the random power flow of the distribution network in the main region can be obtained. ② Solving the random power flow in the subregion When the injected power in the main region and other sub-regions is determined, the boundary voltage in formula (4) will be used. U n.B In sub-region n The internal power injection points are subjected to a first-order Taylor expansion, as shown in equation (10): （10） In the formula, sub-region n The reference value of the boundary voltage after the first-order Taylor expansion; These are the coefficients of the first-order Taylor expansion; It is a sub-region n Inner k The change in injected power at each node; b. After processing in step a, the boundary voltage of the sub-region can be divided into two parts: the reference value caused by power injection at each node of the distribution network and the change value caused by power injection within the sub-region. c. Introduce the sensitivity of each node's power injection to its boundary voltage within the sub-region, and substitute it into formula (10) to obtain the boundary voltage under different power injections in the sub-region; Using the boundary voltage as the root node, the power flow equations are reconstructed under the topology of the subregion, and the stochastic power flow calculation results of the subregion are obtained by solving the equations using the Newton-Raphson iteration method.

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