A power grid network topology planning method and system considering line pi connection

Abstract

The application belongs to the technical field of power grid topology planning, and particularly discloses a power grid network topology planning method and system considering line pi connection, which comprises the following steps: establishing a set of nodes capable of being connected Node_pi, setting a corresponding breaking branch and two-arm branch for each node capable of being connected; using a pi connection optimization variable p to represent whether each node capable of being connected is connected, using a branch on-off variable β to represent whether each to-be-built line is connected; using the pi connection optimization variable p and the branch on-off variable β as optimization variables, taking the minimum active power loss and total construction cost as the target, and constructing a topology planning target function; the total construction cost comprises a branch construction cost and a cost saved by introducing the pi connection; the topology planning target function is solved to obtain a network topology planning result. The 0-1 type optimization variable representing the pi connection is introduced in line planning, the network topology structure considering the pi connection can be obtained, and the construction cost can be greatly reduced.

Description

Technical Field

[0001] This invention relates to the field of power grid topology planning technology, and in particular to a power grid topology planning method and system that takes into account line π-connections. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] As a crucial foundation for the efficient and secure transmission of electrical energy, the planning and design of power grid topology has a significant impact on the safe and stable operation of the power grid. With the transformation of the energy structure and the rapid development of the power system, higher requirements are needed for grid topology planning methods in terms of economy and flexibility.

[0004] π-connection is a node connection method in power systems, referring to the direct connection of a newly built substation or load point to the middle of an existing transmission line, forming a topology resembling the Greek letter "π". This connection method can effectively utilize existing transmission line resources and reduce engineering investment for new node connections. In power grid topology planning, π-connection, as an economical and efficient line connection strategy, is widely used in power grid expansion and system structure optimization in areas with increasing load, enabling the rational evolution of network topology while ensuring system stability.

[0005] Existing power grid planning methods often rely on factors such as load distribution and power generation layout, using mathematical programming or intelligent optimization to construct the topology. However, they fail to consider the application of π-connections in topology planning, resulting in topologies characterized by limited connectivity and a large number of branches, often leading to high planning and construction costs. If π-connections are subsequently incorporated into these established topology schemes, human decision-making is usually required to improve the topology connections, further limiting the efficiency of power grid topology planning. Summary of the Invention

[0006] To address the aforementioned issues, this invention proposes a power grid topology planning method and system that considers π-connections of lines. It introduces 0-1 type optimization variables to represent π-connections, constructs a multi-objective programming model, and establishes π-connection-related constraints to obtain a power grid topology that considers π-connections of lines.

[0007] In some implementations, the following technical solutions are adopted:

[0008] A method for topology planning of a power grid that takes into account π-connections of lines, comprising:

[0009] Establish a set of π-connectable nodes Node_pi, and set the corresponding open and closed branches and two-arm branches for each π-connectable node;

[0010] Optimization variables via π connectionp Whether each π-connectable node is π-connected is indicated by the branch on / off variable. β This indicates whether each planned line is connected.

[0011] Using π as the optimization variable p and branch continuity variables β To optimize the variables, a topology programming objective function is constructed with the goal of minimizing active power loss and total construction cost; the total construction cost includes the cost of branch road construction and the cost saved by introducing π-connections.

[0012] The objective function of the topology planning is solved to obtain the network topology planning result.

[0013] As a further solution, a set of π-connectable nodes, Node_pi, is established, specifically as follows:

[0014] Determine the set of nodes to be connected, calculate the distance from each node in the set to the midpoint of each existing line, select the minimum distance value, and if the minimum distance value is less than the set connectable distance... L pm If so, then the node will be added to the set of connectable nodes, Node_pi.

[0015] As a further solution, each π-connectable node is assigned its corresponding open branch and two-arm branches, specifically as follows:

[0016] For each π-connectable node, calculate its corresponding connection to each existing line. γ Indicators, the γ The index is the difference between the length of the conventional access line corresponding to the π-connectable node and the existing branch, and the sum of the lengths of the two arms of the π-connection access line; all are selected. γ The existing line corresponding to the maximum value in the index is used as the open branch corresponding to the π-connectable node, and then the two arm branches are determined.

[0017] As a further option, the total construction cost is specifically as follows:

[0018] ;

[0019] in, C ij Indicates branch ( I, I The construction cost coefficient of ) β ij Indicates branch ( I, I The on / off state of ); S k This represents the π-connectable node set Node_pi. k Cost-saving coefficient per π contact p kIndicates the first Node in Node_pi k The π-connection state of each π-connector It represents the set of all possible branches.

[0020] As a further option, the objective function of the topology planning is specifically as follows:

[0021] ;

[0022] in, Indicates branch ( I, I The active power loss of ) C sum The total construction cost, w L , w C These are the weighting coefficients for active power loss and total construction cost, respectively.

[0023] As a further option, the weighting coefficients for active power loss and total construction cost are... w L and w C The specific method for determining it is as follows:

[0024] Data on active power loss and total construction cost in existing planning schemes are obtained and normalized to be uniformly converted into dimensionless values ​​in the [0,1] interval.

[0025] Calculate the probability distribution of active power loss data and total construction cost data, and then calculate the degree of variation of active power loss data and total construction cost data respectively;

[0026] Objective weights for active power loss and total construction cost are calculated based on the aforementioned degree of variation.

[0027] A quantitative judgment matrix for active power loss and total construction cost is constructed by representing the relative importance of each indicator through a three-dimensional array.

[0028] By calculating and normalizing the average value of each row of elements in the quantitative judgment matrix, the subjective weights of active power loss and total construction cost are obtained.

[0029] The weighting coefficients for active power loss and total construction cost are obtained by combining the objective and subjective weights. w L and w C .

[0030] As a further step, the degree of variation in active power loss data and total construction cost data is calculated, specifically as follows:

[0031] ;

[0032] in, E j Sub-target j The degree of variation, sub-target j This represents active power loss data or total construction cost data; m represents the number of existing planning schemes. i This indicates the number of the existing planning scheme data group. p ij yes x ij The corresponding probability value, x ij Indicates the first i Sub-goals of existing planning schemes j The normalized value.

[0033] As a further solution, the weighting coefficients for active power loss and total construction cost are obtained by combining the objective weights and subjective weights, as follows:

[0034]

[0035]

[0036] in, , These are the subjective and objective weights of active power loss, respectively. , These are the subjective and objective weights of the total construction cost, respectively. and These are the weighting coefficients for subjective weights and objective weights, respectively.

[0037] As a further option, the constraints of the topology programming objective function include basic constraints and π-connection related constraints, and the π-connection related constraints need to simultaneously satisfy the following conditions:

[0038] (1) The impedance value of each branch becomes the sum of the initial impedance and the change in branch impedance due to the π connection.

[0039] (2) In the set of π-connected disconnected branches, nodes with the same branch number that can be π-connected cannot be π-connected at the same time;

[0040] (3) In the set of π-connected two-arm branches, nodes with the same branch number that can be π-connected cannot be π-connected at the same time;

[0041] (4) A branch cannot simultaneously belong to a π-connected open branch and a π-connected two-arm branch.

[0042] In other embodiments, the following technical solutions are adopted:

[0043] A power grid topology planning system that takes into account π-connections of lines includes:

[0044] The π-connectable node filtering module is configured to establish a set of π-connectable nodes Node_pi, and to set the corresponding open and closed branches and two-arm branches for each π-connectable node.

[0045] The topology planning objective building module is configured to optimize variables via π. p Whether each π-connectable node is π-connected is indicated by the branch on / off variable. β This indicates whether each line to be built is connected; π is used as the optimization variable. p and branch continuity variables β To optimize the variables, a topology programming objective function is constructed with the goal of minimizing active power loss and total construction cost; the total construction cost includes the cost of branch road construction and the cost saved by introducing π-connections.

[0046] The topology planning objective solution module is configured to solve the topology planning objective function to obtain the network topology planning result.

[0047] Compared with the prior art, the beneficial effects of the present invention are:

[0048] (1) In the planning of the line, the present invention introduces 0-1 type optimization variables representing π connection, and at the same time establishes π connection related constraints on the framework of basic constraints to ensure the safe and stable operation of the system, thereby obtaining a network topology that considers π connection, which can greatly reduce construction costs.

[0049] Meanwhile, this invention calculates the minimum distance between each node to be connected and the midpoint of the existing line, selects nodes whose minimum distance is less than a preset value as π-connectable nodes, and selects the best π-connection disconnection branch that matches the π-connectable nodes by calculating evaluation indicators, thereby avoiding errors introduced by subjective judgment and improving the accuracy of π-connection access.

[0050] This invention reduces the complexity of solving the objective function of topology planning by pre-selecting π-connectable nodes and optimal π-connection disconnected branches; at the same time, when carrying out subsequent power grid expansion planning, it can continue to expand based on this set without remodeling, thus reducing the workload of subsequent planning.

[0051] (2) This invention aims to minimize active power loss and total construction cost, constructs a topology planning objective function, and calculates the weights of active power loss and total construction cost based on the original planning scheme data. When calculating the weights, the objective weights are determined based on the degree of data variation, and the subjective weights are obtained through a quantitative judgment matrix. The final weight coefficients of active power loss and total construction cost are obtained by combining the objective weights and the subjective weights. This can avoid the problem that the determination of the weight coefficients is greatly affected by the data parameters, improve the accuracy of the weights, make the decision-making process more reasonable and balanced, and consider the economic efficiency of the project implementation while reducing active power loss.

[0052] Other features and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0053] Figure 1 This is a schematic diagram of the traditional node access method;

[0054] Figure 2 This is the π-connection method in an embodiment of the present invention;

[0055] Figure 3 This is a schematic diagram of the π-connection model in an embodiment of the present invention;

[0056] Figure 4 This is a schematic diagram illustrating the determination of the π-connected disconnected branch in an embodiment of the present invention;

[0057] Figure 5 This is a branch diagram of the 24-node system to be built in an embodiment of the present invention;

[0058] Figures 6(a) and 6(b) show the results of power grid topology planning without considering π-connection and with considering π-connection, respectively. Detailed Implementation

[0059] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0060] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0061] Example 1

[0062] In traditional solutions, when a node to be connected to the power grid, it is usually necessary to construct branch lines from the node to be connected to the nodes on both sides to achieve grid connection; for example... Figure 1 As shown; while π-connection involves disconnecting the existing line and drawing a new line from a new node to connect to the vicinity of the break point, such as... Figure 2 As shown, this wiring method can effectively utilize existing transmission line resources and reduce the engineering investment for new node access to the system.

[0063] Based on this, in one or more embodiments, a power grid topology planning method considering π-connections of lines is disclosed. A 0-1 type optimization variable representing π-connections is introduced to construct a topology planning objective function. At the same time, π-connection related constraints are established on the framework of basic constraints to ensure the safe and stable operation of the system. A mathematical solver is used to solve the planning problem, thereby obtaining the optimized grid topology structure.

[0064] As a specific implementation method, a power grid topology planning method that takes into account π-connections of lines mainly includes the following process:

[0065] S101: Establish a set of π-connectable nodes Node_pi, and set the corresponding open and closed branches and two-arm branches for each π-connectable node.

[0066] Specifically, such as Figure 3 As shown, when defining π connection, the node to be connected to the grid at both ends and the line on the opposite side is disconnected during π connection is called the π-connectable node. The branch on the opposite side that is disconnected due to the π connection of the node is called the π-connection disconnected branch. The two branches connected at both ends of the π-connection node are called the π-connection two-arm branches.

[0067] This embodiment establishes a set of nodes that can be π-connected, Node_pi, which lists the node numbers of all nodes that can be π-connected. It stipulates that only nodes in this set can be considered for π-connection, as shown in the following formula:

[0068] (1)

[0069] Among them, Node_pi i This represents the first π-connectable node in the set Node_pi. i The element, in practice, is the [number]th element. i The node number of each π-connectable node, where N1 is the number of π-connectable nodes.

[0070] As a specific implementation method, when constructing the set of nodes that can be π-connected, if some nodes to be connected are too far from existing lines, then the value of π-connection is relatively low. Therefore, based on the spatial distance index, the distance from each node to be connected to the midpoint of each existing line is calculated, and the minimum distance value is selected, i.e.:

[0071] (2)

[0072] in, L min_i Indicates the first i The minimum distance between a node and an existing line. L ij Indicates the first i The node and the first j The distance of the existing lines, N is the number of all nodes to be connected, and N2 is the number of existing lines.

[0073] If the minimum distance value L min_i Less than the set π-connection distance L pm If so, then the node i is included in the set of connectable nodes Node_pi.

[0074] Furthermore, for each specific π-connectable node, not all branches to be built can be considered for π-connection. If the distance between the π-connectable node and the midpoint of the broken branch is small, the length of the constructed line will also be reduced. In addition, if the length of the broken branch is large, then π-connection can make better use of the existing line, and the advantages of π-connection can be better utilized. This embodiment takes into account the above factors and constructs a mathematical expression for finding the optimal π-connected broken branch.

[0075] Specifically, in combination Figure 4 When a node is connected via conventional access, lines a and b need to be constructed; when connected via π-connection, lines c and d need to be constructed. Therefore, when considering the corresponding open and closed branches and the two arm branches of the π-connection node, it is necessary to find a more economical solution that minimizes the required line length compared to the conventional access method. The construction lengths of the two arm branches c and d of the π-connection node are similar when connected via π-connection; in this embodiment, it is assumed that their lengths are equal (let's say they are equal). L c Assuming the line lengths for normal node access are as follows: L a and L b .

[0076] Based on this, this embodiment sets evaluation indicators for selecting the optimal disconnected branch. γ ij For a π-connectable node i, calculate its evaluation index corresponding to all existing lines. γ ij After comparison, the optimal π-connected open branch corresponding to the π-connectable node can be obtained; after the open branch is determined, the two-arm branch set is also completed.

[0077] π-connectable nodes i With thej Evaluation indicators corresponding to existing lines γ ij The calculation method is as follows:

[0078] (3)

[0079] in, L a_ij , L b_ij , L c_ij These are π-connectable nodes. i With the j The length of the conventional access line corresponding to the existing branch and the length of the two arms of the π-connection access line.

[0080] The existing line corresponding to the maximum value of the evaluation index is selected as the optimal π-connection disconnected branch.

[0081] This embodiment determines the set of possible π-connection nodes and the optimal π-connection disconnection branch, which can avoid errors introduced by subjective judgment and improve the accuracy of evaluating and selecting the optimal π-connection line. At the same time, the evaluation index is calculated based on the difference in line length between π-connection and conventional access during the selection process. Some forward-looking work has been done on the cost-saving part of π-connection in the objective function when solving the optimization problem, which optimizes the problem-solving process and reduces the complexity of solving the objective function.

[0082] This ultimately forms the pre-defined set of π-connected disconnected branches. L dis and π connect the two arm branches set L arm The branches are represented by numbers, and they have the same dimension as Node_pi, as shown in the following formula:

[0083] (4)

[0084] (5)

[0085] in, L dis_i Represents the π-connected open branch set L dis The first in i Each element corresponds to a node with the index Node_pi. i The π-connected open branch number of the node; L arm_i，1、 L arm_i，2 Represents the set of two branches connected to π. L arm No. i The two elements in the row represent the corresponding number Node_pii The two π-connectors of the node are the two arm branches.

[0086] S102: Optimize variables by connecting π p Whether each π-connectable node is π-connected is indicated by the branch on / off variable. β This indicates whether each planned line is connected.

[0087] In this embodiment, branch on / off variables are set respectively. β And π connected to optimization variables p Among them, the branch on / off variables β This indicates whether each planned line is connected or not; β=1 Time indicates connectivity. β=0 Time indicates disconnection; π is connected to the optimization variable. p This is a 0-1 variable representing whether each π-connectable node is π-connected, and it has the same dimension as Node_pi. It indicates whether each π-connectable node is π-connected. When p=1, it means π-connection, and when p=0, it means no π-connection is performed.

[0088] In this embodiment, the ultimate goal of solving the π-connected power grid topology planning problem is to obtain the optimal objective function that satisfies the constraints. β The value of π and the variable π p The value of .

[0089] S103: Using π as the optimization variable p and branch continuity variables β To optimize the variables, a topology programming objective function is constructed with the goal of minimizing active power loss and total construction cost; where the total construction cost includes the cost of branch road construction and the cost saved by introducing π-connections.

[0090] In this embodiment, considering the three aspects of active power loss, line construction cost, and π-connection impact cost, a topology planning objective function is constructed with the goal of minimizing active power loss and total construction cost; where the total construction cost includes branch construction cost and the cost saved by introducing π-connection.

[0091] Specifically, the objective function for topology programming is as follows:

[0092] (6)

[0093] (7)

[0094] in, F The overall objective function is... P loss,ij Indicates branch ( I, I The active power loss of ) C sum The total construction cost,C ij Indicates branch ( I, I The construction cost coefficient of ) β ij Indicates branch ( I, I The on / off state of ) , where Node_pi represents the set of all connectable nodes. S k This represents the π-connectable node set Node_pi. k Cost-saving coefficient per π contact p k Indicates the first Node in Node_pi k The π-connection state of each π-connector Represents the set of all possible branches. w L and w C These represent the weighting coefficients for active power loss and total construction cost, respectively.

[0095] In this embodiment, the weighting coefficients for active power loss and total construction cost are... w L and w C The specific method for determining it is as follows:

[0096] S1031: Obtain data on active power loss and total construction cost from existing planning schemes. To eliminate the dimensional differences between different objectives, normalize the data to convert it into dimensionless values ​​within the [0,1] interval. The normalization method is as follows:

[0097] (8)

[0098] in, i This indicates the number of the existing planning scheme data group. j The value represents the type of sub-objective, and in this embodiment it is 1 or 2 (representing active power loss and total construction cost, respectively). x ij0 It is the first i The first scheme j The original values ​​of each sub-target. x ij It is the normalized value, which takes the value [0,1].

[0099] S1032: Calculate the probability distribution of active power loss data and total construction cost data, and then calculate the degree of variation of active power loss data and total construction cost data respectively.

[0100] Specifically, the formula for calculating the probability distribution is:

[0101] (9)

[0102] Where m is the number of existing planning schemes. p ij yes x ij The corresponding probability value.

[0103] The formula for calculating the degree of variation in data is:

[0104] (10)

[0105] in, E j Sub-target j The degree of variation, E j The smaller the value, the greater the degree of data variation.

[0106] S1033: Calculate the objective weights of active power loss and total construction cost based on the degree of variability.

[0107] The formula for calculating objective weights is as follows:

[0108] (11)

[0109] Among them, w j o It is the first j The objective weight of each sub-goal E j Sub-target j The degree of variation, where k is the index used for summation, k=1 indicates Take the value corresponding to the first sub-target, k=2 means Take the value corresponding to the second sub-target.

[0110] S1034: Use the improved analytic hierarchy process to calculate the subjective weights of active power loss and total construction cost respectively.

[0111] In the traditional analytic hierarchy process (AHP), when constructing the judgment matrix, experts compare the evaluation indicators pairwise to determine the relative importance of each indicator. At this time, experts need to accurately quantify how many times more important indicator a is than indicator b, which is often difficult to determine and can lead to large errors.

[0112] Therefore, this embodiment transforms the one-dimensional elements of the judgment matrix into three-dimensional elements, that is... α =( l , m , u For example, if A is more important than B, it can be represented as (2, 3, 4), meaning that A's importance may be 2, 3, or 4 times that of B. α To determine the elements in the matrix, (l , m , u ) represents a three-dimensional array of elements. l This is the most conservative estimate (lower limit). m For the most likely estimate, u This is the most optimistic estimate (upper limit).

[0113] Calculate the geometric mean of each row in the judgment matrix;

[0114] (12)

[0115] Where j and q are the row and column numbers of the judgment matrix, respectively. This represents the geometric mean of the j-th row, which is the geometric mean of the j-th sub-target. , , Each element in the j-th row represents a three-dimensional array; q takes the value 1 or 2.

[0116] Normalize the geometric mean of each row:

[0117] (13)

[0118] Finally, the subjective weight w of the sub-objective of the j-th objective is obtained. j s :

[0119] (14)

[0120] in, , , They are respectively The corresponding three-dimensional array; The normalized geometric mean. They are The corresponding three-dimensional array.

[0121] S1035: Combining the objective and subjective weights, the weighting coefficients for active power loss and total construction cost are obtained respectively. w L and w C .

[0122] Considering that a large difference between subjective and objective weights could lead to significant weight fluctuations and sensitivity to extreme values, this embodiment employs a weighted summation of the subjective and objective weights, specifically as follows:

[0123] (15)

[0124] Among them, wj o It is the first j The objective weight of each sub-goal, w j s It is the subjective weight of the sub-objective of the j-th objective; and These are their weighting coefficients.

[0125] Assume that active power loss is sub-objective 1 and total construction cost is sub-objective 2.

[0126] The weighting coefficient for active power loss w L Specifically:

[0127] (16)

[0128] Weighting coefficient of total construction cost w C Specifically:

[0129] (17)

[0130] For weighting coefficients and It needs to satisfy α>0, β>0, α+β=1; and, in order to make the comprehensive weight spatially as close as possible to the subjective and objective weights, and to ensure that the subjective and objective weights tend to be consistent, α and β should also satisfy:

[0131] (16)

[0132] Solving for the conditions obtained above and This allows us to ultimately obtain the weighting coefficients for active power loss and total construction cost. w L and w C .

[0133] This embodiment assigns accurate and reliable weight coefficients to the total construction cost of active power loss through a comprehensive processing of subjective and objective weights, making the decision-making process more reasonable and balanced, and can consider the economic efficiency of project implementation while reducing active power loss.

[0134] In actual power grid operation, the values ​​of variables such as branch active and reactive power, branch current, node voltage, branch resistance, and reactance need to satisfy the basic laws of power grid operation. Constraints on these variables are constructed based on actual operational requirements to find a grid topology that meets the actual operational needs of the power grid. Although these variables are not part of the objective function, they are variables that change depending on whether branches are connected or π-connected, and are key optimization variables.β , p There is a coupling relationship.

[0135] When a π-connectable node is π-connected, the π-connection open branch corresponding to that node is disconnected, while the two arms of the π-connection are connected. This illustrates the π-connection variable. p Branch continuity variables β There is a coupling relationship between them. Furthermore, since the π-connection method affects the impedance parameters of the two-arm branches of the π-connection, the relevant parameters of the two-arm branches implementing the π-connection need to be adjusted when constructing constraints. In addition, based on the actual topology of the power grid, a branch cannot simultaneously be a π-connected open branch or a two-arm branch with different π-connectable nodes, nor can it be both an open branch and a two-arm branch. This affects the optimization variables. p This created constraints.

[0136] Therefore, the constraints of the objective function of topology planning in this embodiment can be divided into two categories: one category is the constraints on the rationality of the topology in the power grid topology planning, such as connectivity constraints, power flow constraints, and capacity security constraints. These are the basic constraints that the safe and stable operation of the power grid must meet; the other category is the new constraints on the π-connection variables and related auxiliary optimization variables after the introduction of π-connection. Through these constraints, a mathematical relationship can be established between the π-connection variables and the branch on / off variables, thereby realizing the branch on / off planning that takes π-connection into account.

[0137] Specifically, the basic constraints include:

[0138] (1) Connectivity constraints

[0139] For any network topology, it is necessary to ensure that all nodes are connected in the network and that there are no isolated nodes or branches. Connectivity is described using the form of power flow.

[0140] Create binary variables r i Used to indicate the first i The connectivity status of each node. Define an auxiliary binary variable. fl ij and fl ji , respectively representing from node i arrive j and from node j arrive i The flow rate is used to simulate energy flow in the network. Branch on / off variables are established. β Flow variables fl With node connectivity variables r Mathematical relationship between ， By requiring that the total number of reachable nodes equals the total number of nodes, we ensure that all nodes are reachable.

[0141] (2) Voltage safety constraints

[0142] Constraints are established for the node voltage of each node, limiting it to a reasonable range.

[0143] (14)

[0144] in, V i It means the first i The variable of the node voltage of each node. V min , V max These are the set minimum and maximum node voltage values, respectively.

[0145] (3) Branch capacity constraints

[0146] The maximum capacity of each branch is limited to prevent excessive power from affecting the safe operation of the power grid.

[0147] (15)

[0148] in P ij , Q ij These represent lines work The active and reactive power variables on the surface, S max This is the maximum capacity of the line as set.

[0149] (4) Trend-related constraints

[0150] The relationship between voltage, current, and power is:

[0151] (16)

[0152] in, Let be the node voltage value of node i. This represents the current flowing through branch ij.

[0153] Convex programming optimization problems guarantee the global optimality of the solution in mathematical theory. However, Equation (16) is a nonlinear equality constraint, which is usually difficult to handle in optimization problems. It may cause the optimization problem to become non-convex, making it difficult to find the global optimal solution.

[0154] Second-order cone relaxation is a type of convex relaxation technique. Its main purpose is to relax the original AC power flow formula (16), which is a quadratic constraint, into a second-order cone constraint, making it easier to solve. Auxiliary variables are introduced. αi Represents a node i The square of the voltage, β ij Indicates the route through which the water flows work The square of the current. Therefore:

[0155] (17)

[0156] Equation (17) can be written in the form of a standard second-order cone:

[0157] (18)

[0158] This form of second-order cone constraint is convex, therefore it can be solved using efficient convex optimization algorithms. After transforming the original problem into a second-order cone form, it can be solved using existing optimization software and libraries (such as CVX, MOSEK, Gurobi, etc.). These software and libraries have been optimized for second-order cone programming problems and can efficiently handle large-scale problems.

[0159] Voltage drop equation:

[0160] (19)

[0161] Power balance equation:

[0162] (20)

[0163] in, r ij , x ij They are branch roads work The resistance and reactance parameters, , Let represent the squares of the node voltages at nodes j and i, respectively; It flows through a branch road brother The square of the current value; , They are from the nodes i via branch road two Outflowing active power and power from nodes j via branch road brother Inflow node i The active power; , They are from the nodes i via branch road two Outflowing reactive power and from nodes j via branch road brother Inflow node i The reactive power. , These are the resistance and reactance parameters of branch ji, respectively. , These are nodes i Active and reactive loads; , These are the active power and reactive power injected by the generator at node i, respectively.

[0164] π-related constraints include:

[0165] (1) The introduction of π connection will affect the system parameters. In this embodiment, after considering the π connection of the line, the impedance parameters of the two arms of the π connection will be affected due to the change in the connection method and spatial distance. The default given value cannot be used to continue the calculation, and the impedance value needs to be adjusted accordingly.

[0166] (twenty one)

[0167] in, r ij_π , x ij_π The impedance vectors of each branch are updated based on the influence of the π-connection variable. r ij , x ij This represents the initial impedance values ​​of all branches. p k It represents the branch number in the set of two arm branches. k The 0-1 variable Δ indicates whether the corresponding π-connected node is π-connected. r ij Δ x ij Indicates the branch affected by π connection. work The impedance change value, L arm It is the set of π-connected two-arm branches corresponding to π-connectable nodes.

[0168] This constraint takes into account the impact of π-connection on line impedance, updates relevant line parameters, and makes the system model more closely resemble actual values, resulting in a more accurate solution. Without this consideration, not only would the accuracy of the line power flow equations decrease, affecting the judgment of line current and capacity constraints, but errors would also occur in line cost analysis.

[0169] (2) If multiple nodes are π-connected on the same line, it will not only increase the construction difficulty, but also reduce the reliability of the line and decrease its risk resistance. Therefore, this embodiment limits different π-connection nodes to the same disconnected branch, that is, the nodes with the same branch number in the π-connection disconnected branch set cannot be π-connected at the same time.

[0170] (twenty two)

[0171] in, p i It is a node i Choose whether to connect 0-1 variables with π. Oh j ={ i ∈Node_pi | j = L dis_i} is a π-connected open branch. j The set of corresponding π-connectable nodes (different π-connectable nodes may correspond to the same π-connected open branch; here, the π-connectable node numbers corresponding to the branches in each open branch set are listed), Node_pi is the set of π-connectable nodes. L dis_i It is a π-connectable node i The corresponding π-connected open branch; obviously, for each open branch with two or more corresponding π-connectable nodes. j These π-connectable nodes must be π-connected at most once.

[0172] (3) In order to prevent the line current and capacity from exceeding the requirements after multiple π-connections of a two-arm branch, this embodiment limits that when different π-connection nodes are π-connected, their two-arm branches cannot have a common edge, that is, the nodes that can be π-connected with the same branch number in the set of π-connected two-arm branches cannot be π-connected at the same time.

[0173] (twenty three)

[0174] in, Oh j arm ={ i ∈Node_pi | j = L arm_i} is a π-connected two-arm branch. j The corresponding set of π-connectable nodes (different π-connectable nodes may correspond to the same π-connected two-arm branches; here, the π-connectable nodes corresponding to the branches in each set of two-arm branches are listed). L arm_i It is the corresponding π-connection node in the set of two-arm branches. i The branch number. Clearly, for a two-arm branch with two or more π-connectable nodes... j These π-connectable nodes must be π-connected at most once.

[0175] (4) A branch cannot be both a π-connected open branch and a π-connected two-arm branch at the same time. This is because when a π-connection is made, the π-connected open branch needs to be disconnected, while the π-connected two-arm branch needs to be connected. Therefore, a branch cannot be both open and connected at the same time.

[0176] (twenty four)

[0177] in, i , k These are elements that are distinct from each other in the set of connectable nodes. p i , p k This indicates that the node number is i , k The node's π-connected state is connected to the π-connected variable. L dis_i Indicates the corresponding node in the set of disconnected branches. i Branch road number, L arm_k And represent the corresponding node in the set of two arm branches. k The branch numbering is used to find π-connection nodes that overlap between the two arm branches and the starting branch.

[0178] This constraint limits the attributes of the route during planning, avoids obtaining invalid results in the route topology, and improves the solution speed during planning.

[0179] (5) π connected to variables p Branch continuity variables β There is a topological logical relationship between them, that is, when a node is connected in π, β The corresponding π-connected open branch must be disconnected, and the two arms of the π-connected branch must be connected.

[0180] (25)

[0181] in, β Ldis_i Indicates the corresponding π-connection node i The on / off variables of the open / closed branch, β Larm_i，1 and β Larm_i，2 Indicates the corresponding π-connection node i The on / off variables of the two arms (arm 1 and arm 2).

[0182] This constraint condition considers the relationship between the π connection variable and the line on / off variable, accurately establishes the mathematical equation, clarifies the implementation method of π connection in the power grid structure, and comprehensively considers branch construction and π connection planning, thereby reducing the complexity of model solution.

[0183] Furthermore, in this embodiment, the topology planning modeling for π-connections is considered because the optimization variables for π-connections... p The introduction of this variable introduces nonlinear constraints resulting from the multiplication of optimization variables into the objective function and power balance equations of the model. These constraints require linearization to prevent them from transforming into nonlinear, nonconvex programming. The nonlinear term resulting from the multiplication of optimization variables introduced into the optimization model can be treated as a new nonlinear variable, and linearized using the Big M method.

[0184] For example, in this embodiment, a complex constraint formula of the form (18) appears. It is a formula for calculating active power loss. Due to the introduction of π connection, the impedance becomes a variable related to π connection. p The relevant optimization variables require linearization of the nonlinear terms in the formula.

[0185] (26)

[0186] Analysis shows that the nonlinear constraint can be abstracted into the form of equation (19). The nonlinear constraint that needs to be dealt with is the form of multiplication of continuous variables and 0-1 variables. px ,in p It is a 0-1 optimization variable. x It is a continuously optimizing variable. k It is a constant value. A It is a linear variable.

[0187] (27)

[0188] A new optimization variable can be created using equation (20). NL ,Will px substitution NL, Again NL By adding four linear constraints, the linear variable NL can completely replace the nonlinear term in equation (19). px .

[0189] (28)

[0190] Where M is a very large positive number. p When =0, in the first two constraints NL The value is restricted to x -M and x Between +M, since M is a sufficiently large integer. x The impact is negligible, leading to NL The value is restricted to between -M and M, and can be considered as having no value. NL Constraints are generated. The last two constraints make... NL The limit is 0; when p When =1, the first two constraints make NL Assigned value x The latter two constraints make NL The value is restricted to between -M and M. This transforms it into a linear constraint.

[0191] S104: Solve the objective function of the topology planning to obtain the network topology planning result.

[0192] In this embodiment, based on the established topology planning objective function and constraints, the optimization problem is solved by calling the solver to obtain the network topology planning result.

[0193] The proposed method in this embodiment is applied to a 24-node power system topology planning model. An objective function and constraints considering π-connection are set, an optimization model is established, and the solver gurobi is called to solve it. The optimized topology scheme considering π-connection is used to analyze the system network loss, node voltage and other indicators to verify the feasibility and superiority of the proposed method.

[0194] The initial power system wiring and the topology of the network to be constructed are shown in the figure below. Figure 5 As shown in Figure 6(a) and Figure 6(b), with network loss and construction cost weight coefficients set to 0.5 and 0.5 respectively, the topology planning results of the power grid without considering π-connection and with π-connection are shown in Figure 6(a) and Figure 6(b) respectively; where black circles and line segments represent ordinary nodes and branches, and red dots and lines represent nodes with π-connection and their two π-connection arm branches.

[0195] In performing network loss analysis, this embodiment judges the merits of a solution in terms of network loss by comparing the total network loss. In optimization problems, P loss This represents the active power loss of each branch, which is converted into a double variable with a specific value after solving. The total network loss of the topology scheme can be obtained by summing these variables. In the two schemes mentioned above, the network loss obtained by the scheme without considering π-connections is 12.23MW, while the network loss of the scheme considering π-connections is 11.94MW. It can be seen that under this weight, the scheme considering π-connections reduces network loss by 2.37%, showing a certain advantage.

[0196] In the cost analysis, each pre-constructed branch road has a pre-construction length parameter, and the construction cost is set at 120,000 yuan / km. For each π-connection point, the construction cost can be saved by reducing the required line length when π-connecting. The specific π-connection cost is set according to the specific π-connection situation of each possible π-connection point. These two costs can be calculated through the branch road connection situation in the topology scheme. The total cost is the total construction cost of all branch roads minus the π-connection cost savings. In the above two topology schemes, the total construction cost of the scheme without considering π-connections is 26.97 million yuan, while the total cost of the scheme considering π-connections is 21.66 million yuan, a reduction of 19.6%, which is a significant advantage.

[0197] Example 2

[0198] In one or more embodiments, a power grid topology planning system considering π-connections of lines is disclosed, specifically including:

[0199] The π-connectable node filtering module is configured to establish a set of π-connectable nodes Node_pi, and to set the corresponding open and closed branches and two-arm branches for each π-connectable node.

[0200] The topology planning objective building module is configured to optimize variables via π. p Whether each π-connectable node is π-connected is indicated by the branch on / off variable. β This indicates whether each line to be built is connected; π is used as the optimization variable. p and branch continuity variables β To optimize the variables, a topology programming objective function is constructed with the goal of minimizing active power loss and total construction cost; the total construction cost includes the cost of branch road construction and the cost saved by introducing π-connections.

[0201] The topology planning objective solution module is configured to solve the topology planning objective function to obtain the network topology planning result.

[0202] It should be noted that the specific implementation methods of the above modules are the same as those in Example 1, and will not be described in detail again.

[0203] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for power grid topology planning considering line π connection, characterized in that, include: Establish a set of nodes that can be connected in π, Node_pi, and assign each node its corresponding open / closed branch and two-arm branches; specifically: determining a set of nodes to be accessed, calculating the distance from each node in the set of nodes to be accessed to the midpoint of each existing line, selecting the minimum distance value, and if the minimum distance value is less than a set π accessible distance L pm then the node is included in the set of π accessible nodes Node_pi; for each π accessible node, the corresponding γ indicator of each existing line is calculated, and the γ indicator is the difference between the length of the conventional access line corresponding to the π accessible node and the existing branch and the length of the two-arm line of the π access Selecting all γ The maximum value in the index corresponds to the existing line, which is the open branch corresponding to the connection node, and then the two-arm branch is determined. Optimize variables by π connection p Indicate whether each π connectable node is connected by a branch on-off variable β Indicate whether each line to be built is connected Optimizing variables with π p and branch on-off variables β Topology planning objective function is constructed with the objective of minimizing the weighted sum of active power loss and total construction cost, taking the optimizing variables as π The total construction cost includes the cost of branch road construction and the cost saved by introducing π-connections; Solving the objective function of the topology planning yields the network topology planning result; Weighting factors for active power losses and total construction costs w L and w C The determination method is specifically: Data on active power loss and total construction cost in existing planning schemes are obtained and normalized to be uniformly converted into dimensionless values ​​in the [0,1] interval. Calculate the probability distribution of active power loss data and total construction cost data, and then calculate the degree of variation of active power loss data and total construction cost data respectively; Objective weights for active power loss and total construction cost are calculated based on the aforementioned degree of variation. A quantitative judgment matrix for active power loss and total construction cost is constructed by representing the relative importance of each indicator through a three-dimensional array. By calculating and normalizing the average value of each row of elements in the quantitative judgment matrix, the subjective weights of active power loss and total construction cost are obtained. The objective weight and the subjective weight are combined to obtain weight coefficients of the active loss and the total construction cost respectively w L and w C .

2. The power grid topology planning method considering π-connections of lines as described in claim 1, characterized in that, The total construction cost is as follows: ； in, C ij Indicates branch ( i,j The construction cost coefficient of ) β ij Indicates branch ( i,j The on / off state of ); S k This represents the π-connectable node set Node_pi. k Cost-saving coefficient per π contact p k Indicates the first Node in Node_pi k The π-connection state of each π-connector It represents the set of all possible branches.

3. The power grid topology planning method considering π-connections of lines as described in claim 1, characterized in that, The objective function of the topology programming is specifically: ； in, Indicates branch ( i,j The active power loss of ) C sum The total construction cost, w L , w C These are the weighting coefficients for active power loss and total construction cost, respectively.

4. The power grid topology planning method considering π-connections of lines as described in claim 1, characterized in that, The degree of variation in active power loss data and total construction cost data was calculated, specifically as follows: ； in, E j Sub-target j The degree of variation, sub-target j This represents active power loss data or total construction cost data; m represents the number of existing planning schemes. i This indicates the number of the existing planning scheme data group. p ij yes x ij The corresponding probability value, x ij Indicates the first i Sub-goals of existing planning schemes j The normalized value.

5. The power grid topology planning method considering π-connections of lines as described in claim 1, characterized in that, The weighting coefficients for active power loss and total construction cost are obtained by combining the objective and subjective weights, respectively, as follows: in, , These are the subjective and objective weights of active power loss, respectively. , These are the subjective and objective weights of the total construction cost, respectively. and These are the weighting coefficients for subjective weights and objective weights, respectively.

6. The power grid topology planning method considering π-connections of lines as described in claim 1, characterized in that, The constraints of the topology programming objective function include basic constraints and π-connection related constraints. The π-connection related constraints must simultaneously satisfy the following conditions: (1) The impedance value of each branch becomes the sum of the initial impedance and the change in branch impedance due to the π connection. (2) In the set of π-connected disconnected branches, nodes with the same branch number that can be π-connected cannot be π-connected at the same time; (3) In the set of π-connected two-arm branches, nodes with the same branch number that can be π-connected cannot be π-connected at the same time; (4) A branch cannot simultaneously belong to a π-connected open branch and a π-connected two-arm branch.

7. A power grid topology planning system considering π-connections of lines, characterized in that, include: The π-connectable node filtering module is configured to establish a set of π-connectable nodes Node_pi, and to set the corresponding open and closed branches and two-arm branches for each π-connectable node. The topology planning objective building module is configured to optimize variables via π. p Whether each π-connectable node is π-connected is indicated by the branch on / off variable. β This indicates whether each line to be built is connected; π is used as the optimization variable. p and branch continuity variables β To optimize the variables, a topology programming objective function is constructed with the goal of minimizing active power loss and total construction cost. The total construction cost includes the cost of branch road construction and the cost saved by introducing π-connections; The topology planning objective solution module is configured to solve the topology planning objective function to obtain the network topology planning result.

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