An economic optimization planning method and system for offshore wind farm power collection system

Abstract

The present invention discloses a method and system for economic optimization planning of an offshore wind farm collection system. The method includes constructing objective functions of cable cost, power loss, and expected ungenerated power cost for the collection system based on offshore wind farm data, constructing an augmented Lagrangian function as a new objective function, initially dividing wind turbines into feeders, and decomposing the new objective function into multiple feeder sub-problems based on the alternating direction multiplier method; treating the collection system as a heterogeneous topology consisting of radial and ring-shaped cables, adding heterogeneous topological constraints to each feeder sub-problem; and iteratively solving the optimal topological structure and total cost of the feeder sub-problem. The present invention aims to implement heterogeneous topological design planning that combines radial and ring structures for offshore wind farm collection systems, decompose the planning problem into multiple sub-problems and perform distributed computing to improve the solution speed and solution quality, thereby achieving economic optimization planning of offshore wind farm collection systems.

Description

Technical Field

[0001] The present invention relates to the technical field of design and planning of power collection systems for offshore wind farms, and in particular to a method and system for economically optimal planning of power collection systems for offshore wind farms. Background Art

[0002] The collection system bridges the gap between offshore wind farms and the onshore power grid. It transmits electricity collected offshore to onshore substations via submarine cables and other equipment. The continuous expansion of offshore wind farms and their installed capacity has led to an increasing difficulty in planning and designing the collection system. The design of the collection system involves not only decisions such as cable routing and cable type selection, but also the impact of power loss on operating costs. While the existing scanning-based partitioning followed by path planning approach can decompose the wind farm collection system planning problem into multiple subproblems and solve them separately, improving solution speed, it fails to consider the coupling relationships between the paths within each subproblem, resulting in low solution accuracy. Mixed-integer quadratic programming can ensure global optimality for small wind farms. However, as wind farms scale, finding the global optimal solution within a feasible timeframe becomes unfeasible. Therefore, finding a distributed computing approach while ensuring both solution speed and accuracy has become a critical technical challenge that needs to be addressed.

[0003] The main structures of existing offshore wind farm power collection systems are radial and ring. Although the radial network structure is simple and low-cost, its reliability is not high. As offshore wind farms develop towards large-scale and deep-sea development, the failure rate and repair time increase, and the power outage losses caused by failures become more serious. The ring structure can ensure that the wind turbine will not be disconnected from the grid after a single cable failure, and has high reliability. However, the ring structure has excessive redundancy and excessive investment costs. The existing power collection system design and planning method adopts a single radial structure or ring structure, which cannot realize the heterogeneous topology design and planning that combines radial and ring structures. Summary of the Invention

[0004] Technical problem to be solved by the present invention: In response to the above-mentioned problems of the prior art, a method and system for economic optimal planning of an offshore wind farm collection system are provided. The present invention aims to realize heterogeneous topology design planning that combines radial structure and ring structure for an offshore wind farm collection system, decompose the planning problem into multiple sub-problems and perform distributed calculations to improve the solution speed and solution quality, thereby realizing economic optimal planning of an offshore wind farm collection system.

[0005] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0006] A method for economic optimization planning of an offshore wind farm power collection system comprises the following steps:

[0007] S1, obtain wind farm data of offshore wind farms;

[0008] S2, based on the wind farm data of the offshore wind farm, construct the objective functions of cable cost, power loss and expected ungenerated energy cost for the collection system respectively, and add them together to obtain the objective function of the total cost;

[0009] S3, based on the total cost objective function, an augmented Lagrangian function is constructed as a new objective function. The wind turbines of the offshore wind farm are initially divided into a single feeder. The new objective function is decomposed into multiple feeder sub-problems based on the alternating direction multiplier method.

[0010] S4, considers the collection system as a heterogeneous topology consisting of radial cables and ring cables, and adds heterogeneous topology constraints to each feeder subproblem;

[0011] S5, using the solver to obtain the optimal topology and total cost of each feeder subproblem;

[0012] S6, update the dual variables in the augmented Lagrangian function;

[0013] S7, judging whether the preset iteration end condition is met, if not, jumping to step S3; otherwise, outputting the optimal topology structure and total cost corresponding to each feeder of the collection system.

[0014] Optionally, the functional expression of the objective function of cable cost, power loss and expected ungenerated energy cost constructed in step S2 is:

[0015] ,

[0016] ,

[0017] ,

[0018] in, is the objective function of cable cost, is the objective function of power loss, is the objective function of the expected cost of ungenerated electricity, is the three-dimensional variable matrix of the radial cable, the three-dimensional variable matrix Elements in is the binary sorting variable of the cable between wind turbines i and j when the maximum sorting position is p, is the three-dimensional variable matrix of the ring cable, the three-dimensional variable matrix Elements in is the binary sorting variable of the cable between wind turbines i and j when the maximum sorting position is q. The binary sorting variable takes the value of 1 or 0 to indicate whether the corresponding cable is built. and are the cost and resistance of the cable between fans i and j in the radial cable section when the maximum sorting position is p, and are the cost and resistance of the cable between fans i and j in the ring cable when the maximum sorting position is q, is the length of the cable between fans i and j, For cable assembly, is a set of bidirectional sequence positions of the cable, including positive and negative sequence positions. The maximum sequence position in the radial portion of the cable is equal to the cable sequence position, and the maximum sequence position in the annular portion of the cable is the larger value of the positive and negative sequence positions. The cables between fans i and j in the radial part of the cable are arranged in the center. The power flowing under normal operating conditions is The cable between fans i and j in the ring cable is in the center sorting position The power flowing under normal operating conditions, the center sorting position of the radial part cable Equal to the maximum sorting position, the center sorting position of the ring section cable is equal to the average of the positive and negative sort positions, is the mean time to repair a cable fault, is the cable failure rate, This is the radial portion of the cable.

[0019] Optionally, step S3 includes:

[0020] S3.1, based on the objective function of the total cost, construct the Lagrangian function of the objective function shown in the following formula:

[0021] ,

[0022] in, is the Lagrangian function of the objective function, is the objective function of the total cost, For the fan assembly, is the dual variable of wind turbine i, Radial network The binary variable of the cable between wind turbine i and wind turbine j, the binary variable takes the value of 1 or 0 to indicate whether the cable is disconnected, the radial network A unidirectionally connected radial network formed by removing a "broken line" in a heterogeneous topology consisting of radial cables and ring cables. The "broken line" refers to the outgoing line of the root node of the ring cable.

[0023] S3.2, based on the Lagrangian function of the objective function, an augmented Lagrangian function is constructed as the new objective function:

[0024] ,

[0025] in, is the augmented Lagrangian function, is the penalty factor;

[0026] S3.3, initially divide the wind turbines in the offshore wind farm into a single feeder. Based on the alternating direction multiplier method, the new objective function is decomposed into multiple feeder subproblems. The function expression of the feeder subproblem for any feeder f is obtained as follows:

[0027] ,

[0028] , ,

[0029] in, is the feeder subproblem for any feeder f, is the objective function of the total cost of feeder f, is a three-dimensional variable matrix The part of the feeder f, is a three-dimensional variable matrix The part of the feeder f, For all wind turbines on feeder f, is the dual variable of wind turbine i on feeder f, is the sum of the binary variables of all outgoing lines of wind turbine i on feeder f, Radial network The binary variable of the cable between wind turbine i and wind turbine j on feeder f, is the sum of the binary variables of all outgoing lines of wind turbine i except the wind turbine on feeder f, For offshore wind farms, except for wind turbines on feeder f, Radial network The binary variable of the cable between wind turbines i and j on feeder f is removed from the equation. The binary variable takes the value 1 or 0 to indicate whether the cable is disconnected.

[0030] Optionally, when adding heterogeneous topology constraints for each feeder sub-problem in step S4, the heterogeneous topology constraints include heterogeneous topology feeder constraints, ring constraints on the heterogeneous topology, and radial network constraints after the "broken lines" on the heterogeneous topology are removed. The radial network constraints after the "broken lines" on the heterogeneous topology are removed include radial network constraints after the forward "broken lines" are removed and radial network constraints after the reverse "broken lines" are removed.

[0031] Optionally, the heterogeneous topology feeder constraints include: (1) a transformer node has at most one incoming line, and each feeder sub-problem has at most one feeder; (2) the outgoing lines of all wind turbine nodes are 0-2 to limit a feeder to at most one ring; (3) the transformer node is the root node; (4) the wind turbine node with an outgoing line equal to 2 is the root node; (5) the wind turbine node with an outgoing line less than or equal to 1 is a non-root node; the ring constraints on the heterogeneous topology include: (6) the ring is part of the original feeder; (7) the outgoing lines of all nodes on the ring are equal to the incoming lines; (8) the outgoing lines of the transformer node on the ring are equal to the outgoing lines of the transformer node of the original feeder; (9) the outgoing lines of other root nodes on the ring are equal to the outgoing lines of other root nodes of the original feeder minus 1; (10) the radial part and the ring part constitute the feeder; (11) a cable on the radial part can only correspond to one maximum sequence position; (12) a cable on the ring part can only correspond to one maximum sequence position.

[0032] Optionally, the radial network constraints after the forward "break" is removed include: (13) the "break" in the forward direction must be on the ring; (14) the "break" in the forward direction can only be the outgoing line of the root node; (15) the radial feeder formed after the "break" in the forward direction is removed; (16) the forward power flow of the radial topology is conserved; (17) each cable occupies exactly one positive sorting position in the forward direction; (18) in the radial network in the forward direction, the number of outgoing lines of the wind turbine node does not exceed one; constraints (16) to (18) are used to ensure that a unidirectionally connected radial network is formed after the "break" is removed in the forward direction; the radial network constraints after the reverse "break" is removed include: (19) the ring of the feeder f in the forward direction is transposed The circular part in the reverse direction is obtained; (20) the radial network formed after removing the "broken line" in the reverse direction is equal to the original network minus the ring in the forward direction plus the ring in the reverse direction minus the "broken line" in the reverse direction; (21) the "broken line" in the reverse direction must be on the ring; (22) the "broken line" in the reverse direction can only be the outgoing line of the root node; (23) the radial feeder formed after removing the "broken line" in the reverse direction; (24) the reverse power flow of the radial topology is conserved; (25) each cable occupies exactly one positive sorting position in the reverse direction; (26) in the radial network in the reverse direction, the number of outgoing lines of the wind turbine node does not exceed one; where constraints (24) to (26) are used to ensure that a unidirectionally connected radial network is formed after removing the "broken line" in the reverse direction.

[0033] Optionally, the function expression for updating the dual variable in the augmented Lagrangian function in step S6 is:

[0034] ,

[0035] in, and are the dual variables of wind turbine i at the n+1th and nth iterations respectively. , is the penalty factor, is the set of feeders, is the sum of the binary variables of all outgoing lines of wind turbine i on feeder f at the nth iteration, For all wind turbines on feeder f; when determining whether the preset iteration end condition is met in step S7, the preset iteration end condition is that the number of iterations is equal to the preset threshold, and the residual of the original problem is equal to Less than the convergence judgment value , or the residual of the original problem and the dual problem Less than the convergence judgment value , where the original problem refers to the objective function of the total cost of feeder f, and the dual problem is the objective function obtained by removing the quadratic penalty term from the augmented Lagrangian function. The residual of the original problem is The calculation function expression is:

[0036] ,

[0037] in, is the residual of the original problem at the n+1th iteration, is the sum of the binary variables of all outgoing lines of wind turbine i on feeder f at the n+1th iteration; the residual of the original problem and the dual problem The calculation function expression is:

[0038] .

[0039] In addition, the present invention also provides an offshore wind farm collection system economic optimization planning system, including an interconnected microprocessor and a memory, and the microprocessor is programmed or configured to execute the offshore wind farm collection system economic optimization planning method.

[0040] In addition, the present invention also provides a computer-readable storage medium, which stores a computer program or instruction, and the computer program or instruction is programmed or configured to execute the economic optimal planning method of the offshore wind farm collection system through a processor.

[0041] In addition, the present invention also provides a computer program product, including a computer program or instructions, which are programmed or configured to execute the economic optimization planning method for the offshore wind farm collection system through a processor.

[0042] Compared with the prior art, the present invention can mainly achieve the following beneficial effects:

[0043] 1. Each substation area contains multiple feeders and dozens of wind turbines, which poses a huge computational challenge. The present invention constructs an augmented Lagrangian function based on the total cost objective function as a new objective function, initially groups the offshore wind farm's wind turbines under a single feeder, decomposes the new objective function into multiple feeder subproblems based on the alternating direction multiplier method (ADMM), adds heterogeneous topological constraints to each feeder subproblem and solves it, and employs the alternating direction multiplier method (ADMM) to decompose the optimization problem of a single substation area into multiple feeder subproblems for distributed computing. The correlations between the subproblems are coordinated by updating the dual variables in the augmented Lagrangian function, significantly improving solution efficiency while ensuring solution accuracy. This decomposes the design and planning problem of the offshore wind farm collection system into multiple subproblems and distributes the computation to improve solution speed and quality, thereby achieving optimal economic planning for the offshore wind farm collection system.

[0044] 2. The present invention includes treating the collection system as a heterogeneous topology consisting of radial cables and ring cables, and can implement a heterogeneous topology design and planning that combines radial and ring structures for the offshore wind farm collection system. A ring structure can be used in areas where wind turbines are concentrated to improve reliability, while a radial structure can be used in peripheral areas to reduce costs. There is no need for a pre-set radial or ring structure, and the cable layout of the wind farm collection system can be adaptively adjusted. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 Schematic diagram of the basic process of the method of the embodiment of the present invention.

[0046] Figure 2 1 are the annual average output power curves of two offshore wind farms in an embodiment of the present invention, (a) is the annual average output power curve of an offshore wind farm equipped with 30 wind turbines, and (b) is the annual average output power curve of an offshore wind farm equipped with 42 wind turbines.

[0047] Figure 3 The following is a comparison of the optimal topological structures of the offshore wind farm collection system equipped with 30 wind turbines in an embodiment of the present invention obtained by different methods, where (a) is a radial topology obtained based on the mathematical programming method, (b) is a ring topology obtained based on the mathematical programming method, and (c) is a heterogeneous topology obtained based on the method of this embodiment.

[0048] Figure 4 The following is a comparison of the optimal topological structures of the offshore wind farm collection system equipped with 42 wind turbines in an embodiment of the present invention obtained by different methods, where (a) is a radial topology obtained based on the mathematical programming method, (b) is a ring topology obtained based on the mathematical programming method, and (c) is a heterogeneous topology obtained based on the method of this embodiment.

[0049] Figure 5 1 are curves showing the number of iterations and the total cost for two offshore wind farms in an embodiment of the present invention. (a) is the curve showing the number of iterations and the total cost for an offshore wind farm equipped with 30 wind turbines, and (b) is the curve showing the number of iterations and the total cost for an offshore wind farm equipped with 42 wind turbines. DETAILED DESCRIPTION

[0050] In order to enable those skilled in the art to better understand the technical solution of the present invention, the technical solution of the present invention will be further described in detail below with reference to the accompanying drawings in the embodiments of the present invention.

[0051] like Figure 1 As shown, the economic optimization planning method for the offshore wind farm power collection system of this embodiment includes the following steps:

[0052] S1, obtain wind farm data of offshore wind farms;

[0053] S2, based on the wind farm data of the offshore wind farm, construct the objective functions of cable cost, power loss and expected ungenerated energy cost for the collection system respectively, and add them together to obtain the objective function of the total cost;

[0054] S3, based on the total cost objective function, an augmented Lagrangian function is constructed as a new objective function. The wind turbines of the offshore wind farm are initially divided into a single feeder. The new objective function is decomposed into multiple feeder sub-problems based on the alternating direction multiplier method.

[0055] S4, considers the collection system as a heterogeneous topology consisting of radial cables and ring cables, and adds heterogeneous topology constraints to each feeder subproblem;

[0056] S5, using the solver to obtain the optimal topology and total cost of each feeder subproblem;

[0057] S6, update the dual variables in the augmented Lagrangian function;

[0058] S7, judging whether the preset iteration end condition is met, if not, jumping to step S3; otherwise, outputting the optimal topology structure and total cost corresponding to each feeder of the collection system.

[0059] The functional expression of the objective function of cable cost, power loss and expected ungenerated energy cost constructed in step S2 of this embodiment is:

[0060] ,

[0061] ,

[0062] ,

[0063] in, is the objective function of cable cost, is the objective function of power loss, is the objective function of the expected cost of ungenerated electricity, is the three-dimensional variable matrix of the radial cable, the three-dimensional variable matrix Elements in is the binary sorting variable of the cable between wind turbines i and j when the maximum sorting position is p, is the three-dimensional variable matrix of the ring cable, the three-dimensional variable matrix Elements in is the binary sorting variable of the cable between wind turbines i and j when the maximum sorting position is q. The binary sorting variable takes the value of 1 or 0 to indicate whether the corresponding cable is built. and are the cost and resistance of the cable between fans i and j in the radial cable section when the maximum sorting position is p, and are the cost and resistance of the cable between fans i and j in the ring cable when the maximum sorting position is q, is the length of the cable between fans i and j, For cable assembly, is a set of bidirectional sequence positions of the cable, including positive and negative sequence positions. The maximum sequence position in the radial portion of the cable is equal to the cable sequence position, and the maximum sequence position in the annular portion of the cable is the larger value of the positive and negative sequence positions. The cables between fans i and j in the radial part of the cable are arranged in the center. The power flowing under normal operating conditions is The cable between fans i and j in the ring cable is in the center sorting position The power flowing under normal operating conditions, the center sorting position of the radial part cable Equal to the maximum sorting position, the center sorting position of the ring section cable is equal to the average of the positive and negative sort positions, is the mean time to repair a cable fault, is the cable failure rate, This is the radial portion of the cable.

[0064] Considering the heterogeneous topology of the power collection system designed and planned in this embodiment, which includes both ring and radial structures, the cable cost and power loss cost calculation methods of these two structures are significantly different. Furthermore, the ring structure does not consider the expected ungenerated energy (EENG) cost. Therefore, the total cost is calculated by independently calculating the cost of each structure and then adding the results, that is, the objective function of cable cost is: The cost of the radial cable and the cost of the ring section cable The sum of the cost of the radial cable and the cost of the ring section cable The function expression is:

[0065] ,

[0066] ,

[0067] in, For the radial part of the cable, For the ring part of the cable, the superscript and subscript in the above text and The following are cable identifiers for the radial and ring sections, respectively. While radial topologies are only required to operate reliably under normal operating conditions, ring topologies must meet the N-1 principle (i.e., the system must function normally after any cable fault is isolated). The most economical cable type is selected based on this principle. To achieve this, the concept of cable sorting position is introduced. In a radial network, the sorting position of a cable is equal to the number of wind turbines downstream of that cable. In radial topologies, the sorting position of a cable coincides with the maximum sorting position. For ring networks, which must meet the N-1 principle under all fault scenarios, positive and negative sorting positions are defined: a positive sorting position is the sorting value after isolating the nearest faulty cable, moving clockwise from the ring root (the transformer node on the ring, or the node closest to the transformer when the transformer is not on the ring), while a negative sorting position is the sorting value after isolating the nearest faulty cable, moving counterclockwise. Cable selection for each topology is determined by the maximum value of the positive and negative sorting positions (i.e., the maximum sorting position).

[0068] Objective function of power loss The power loss of the radial cable and power loss of the ring cable The sum of the power loss of the radial cable and power loss of the ring cable The function expression is:

[0069] ,

[0070] ,

[0071] , ,

[0072] Among them, the maximum sorting position and the center sorting position of the radially distributed cable are equal, so the center sorting position of the radial part of the cable is Equal to the maximum sort position p, is the wind turbine power. For a radial network, under normal operating conditions, the power flowing through a cable equals the product of its sorting position and the average wind turbine power. For a ring section, since the power flow is bidirectional, the central wind turbine (one for an odd number of wind turbines in the ring, two for an even number) is used as the power origin, and power is distributed equally to the transformer nodes on both sides. The center sorting position is defined as the average of the positive and negative sorting positions. Under normal operating conditions, the power flowing through a cable in a ring section equals the product of its center sorting position and the average wind turbine power. The center sorting position of a radial section coincides with its positive and negative sorting positions.

[0073] In this embodiment, step S3 includes:

[0074] S3.1, based on the objective function of the total cost, construct the Lagrangian function of the objective function shown in the following formula:

[0075] ,

[0076] in, is the Lagrangian function of the objective function, is the objective function of the total cost, For the fan assembly, is the dual variable of wind turbine i, Radial network The binary variable of the cable between wind turbine i and wind turbine j, the binary variable takes the value of 1 or 0 to indicate whether the cable is disconnected, the radial network A unidirectionally connected radial network is formed by removing a "break" in a heterogeneous topology consisting of radial and ring cables. The "break" refers to the outgoing cable at the root node of the ring cable. The "break" must meet three requirements: the first requirement is that it is on the ring, the second requirement is that it is the outgoing cable at the root node, and the third requirement is that a unidirectionally connected radial network is formed after the break.

[0077] S3.2, based on the Lagrangian function of the objective function, an augmented Lagrangian function is constructed as the new objective function:

[0078] ,

[0079] in, is the augmented Lagrangian function, is the penalty factor, which includes the quadratic penalty term:

[0080] ;

[0081] S3.3, initially divide the wind turbines in the offshore wind farm into a single feeder. Based on the alternating direction multiplier method, the new objective function is decomposed into multiple feeder subproblems. The function expression of the feeder subproblem for any feeder f is obtained as follows:

[0082] ,

[0083] ,

[0084] in, is the feeder subproblem for any feeder f, is the objective function of the total cost of feeder f, is a three-dimensional variable matrix The part of the feeder f, is a three-dimensional variable matrix The part of the feeder f, For all wind turbines on feeder f, is the dual variable of wind turbine i on feeder f, is the sum of the binary variables of all outgoing lines of wind turbine i on feeder f, Radial network The binary variable of the cable between wind turbine i and wind turbine j on feeder f, is the sum of the binary variables of all outgoing lines of wind turbine i except the wind turbine on feeder f, For offshore wind farms, except for wind turbines on feeder f, Radial network The binary variable of the cable between wind turbines i and j on feeder f is removed from the equation. The binary variable takes the value 1 or 0 to indicate whether the cable is disconnected.

[0085] When adding heterogeneous topology constraints to each feeder sub-problem in step S4 of this embodiment, the heterogeneous topology constraints include heterogeneous topology feeder constraints, ring constraints on the heterogeneous topology, and radial network constraints after the "broken lines" on the heterogeneous topology are removed. The radial network constraints after the "broken lines" on the heterogeneous topology are removed include radial network constraints after the forward "broken lines" are removed and radial network constraints after the reverse "broken lines" are removed.

[0086] In this embodiment, the heterogeneous topology feeder constraints include:

[0087] (1) A transformer node has at most one incoming line, and each feeder subproblem has at most one feeder; this can be expressed as:

[0088] ,

[0089] in, is the binary variable of the cable between wind turbine j and wind turbine i on feeder f, is the set of transformer nodes on feeder f;

[0090] (2) The outgoing lines of all wind turbine nodes are 0-2 to limit a maximum of one ring on a feeder; it can be expressed as:

[0091] ;

[0092] (3) The transformer node is the root node; it can be expressed as:

[0093] ,

[0094] in, It is a binary variable indicating whether wind turbine i is a root node, and its value is 1 or 0, indicating whether it is a root node;

[0095] (4) The wind turbine node with 2 outgoing lines is the root node; it can be expressed as:

[0096] ;

[0097] (5) The node with less than or equal to 1 outgoing line is a non-root node; it can be expressed as:

[0098] .

[0099] In this embodiment, the ring constraints on the heterogeneous topology include:

[0100] (6) The ring is a part of the original feeder; it can be expressed as:

[0101] ,

[0102] in, is a binary variable of the cable between fans i and j in the ring section of the cable on feeder f;

[0103] (7) All nodes on the ring have outgoing lines equal to incoming lines; this can be expressed as:

[0104] ,

[0105] in, is a binary variable for the cable between fan j and fan i in the ring section of the feeder f;

[0106] (8) The outgoing line of the ring transformer node is equal to the outgoing line of the original feeder transformer node; it can be expressed as:

[0107] ;

[0108] (9) The outgoing lines of other root nodes on the ring are equal to the outgoing lines of other root nodes of the original feeder minus 1; it can be expressed as:

[0109] ,

[0110] in, is the set of wind turbines on feeder f;

[0111] (10) The radial part and the ring part constitute the feeder; it can be expressed as:

[0112] ,

[0113] in, is a binary variable for the cable between wind turbine j and wind turbine i in the radial part of the cable on feeder f;

[0114] (11) A cable on the radial part can only correspond to one maximum sequence position; it can be expressed as:

[0115] ,

[0116] in, is the binary sorting variable of the cable between wind turbines i and j in the radial section of the cable on feeder f at the maximum sorting position p;

[0117] (12) A cable on the ring section can only correspond to one maximum sequence position; it can be expressed as:

[0118] ,

[0119] in, is the binary sorting variable of the cable between fans i and j in the ring section of the cable on feeder f at the maximum sorting position q.

[0120] In this embodiment, the radial network constraints after the forward “breaks” are removed include:

[0121] (13) In the positive direction, “breaking the line” must be on the ring; it can be expressed as:

[0122] ,

[0123] in, is a binary variable of the cable between wind turbine j and wind turbine i on feeder f, which is the positive “broken line”;

[0124] (14) In the forward direction, the only “broken line” is the outgoing line of the root node; it can be expressed as:

[0125] ;

[0126] (15) The radial feeder formed after the “broken line” in the forward direction is removed can be expressed as:

[0127] ;

[0128] (16) Forward power flow conservation in radial topology can be expressed as:

[0129] ,

[0130] in, is the number of forward or reverse sequence positions of the cable, is the binary variable of the cable between wind turbine i and wind turbine j at the forward sequential position k of feeder f, is a binary variable of the cable between wind turbine j and wind turbine i with forward sequence position k on feeder f, where k is the forward sequence position;

[0131] (17) In the positive direction, each cable occupies exactly one positive sorting position; it can be expressed as:

[0132] ;

[0133] (18) In a radial network with a positive orientation, the number of outgoing lines from a wind turbine node does not exceed one; this can be expressed as:

[0134] ;

[0135] Constraints (16) to (18) are used to ensure that a unidirectionally connected radial network is formed after removing the "broken wires" in the forward direction.

[0136] In this embodiment, the radial network constraints after the reverse “break” is removed include:

[0137] (19) Transpose the loop of the feeder f in the forward direction to obtain the loop part in the reverse direction; it can be expressed as:

[0138] ,

[0139] in, is a binary variable of the cable between wind turbine i and wind turbine j on the loop portion of the cable in the reverse direction of feeder f;

[0140] (20) After removing the “broken line” in the reverse direction, the radial network to be formed is equal to the original network minus the ring in the forward direction plus the ring in the reverse direction minus the “broken line” in the reverse direction; it can be expressed as:

[0141] ,

[0142] in, is the binary variable of the cable between fans i and j on the radial network formed after the “broken wires” are removed in the reverse direction, is a binary variable of the cable between wind turbine i and wind turbine j that is “broken” in the opposite direction of feeder f;

[0143] (21) In the reverse direction, “breaking the line” must be on the ring; it can be expressed as:

[0144] ;

[0145] (22) In the reverse direction, the “disconnection” can only be the outgoing line of the root node; it can be expressed as:

[0146] ;

[0147] (23) The radial feeder formed after the “broken line” is removed in the reverse direction can be expressed as:

[0148] ;

[0149] (24) Conservation of reverse power flow in radial topology can be expressed as:

[0150] ,

[0151] in, is a binary variable of the cable between wind turbine i and wind turbine j with reverse sequence position h of feeder f, where h is the reverse sequence position;

[0152] (25) In the reverse direction, each cable occupies exactly one positive sorting position; it can be expressed as:

[0153] ;

[0154] (26) In the radial network in the reverse direction, the number of outgoing lines from the wind turbine node does not exceed one; it can be expressed as:

[0155] ;

[0156] Constraints (24) to (26) are used to ensure that a unidirectionally connected radial network is formed after removing the "broken line" in the reverse direction.

[0157] In the above constraints, the matching relationship of each sequence number is as follows:

[0158] Matching relationship (17): ,

[0159] Matching relationship (28): ,

[0160] Matching relationship (29): ,

[0161] Matching relationship (30): ,

[0162] Where p and q are the maximum sorting positions of the cables for the radial and ring sections, respectively. and The center sorting positions of the radial and ring cables are shown, and there is a center sorting position of the radial cable. is equal to the maximum sorting position p of the radial part cable. k and h represent the forward and reverse sorting positions of the network, respectively. Matching relationship (27) indicates that the part where the forward and reverse cables of the collection system flow in the same direction (both flow from i to j) is the radial part, and the part where the forward and reverse cables of the collection system flow in opposite directions is the ring part. Matching relationship (28) indicates that the maximum sorting position and center sorting position of the radial part cable are equal to its forward and reverse sorting positions. Matching relationship (29) indicates that the maximum sorting position of the ring part cable is equal to the maximum value of its forward and reverse sorting positions. Matching relationship (30) indicates that the center sorting position of the ring part cable is equal to the average of its forward and reverse sorting positions.

[0163] The function expression of the dual variable in the updated augmented Lagrangian function in step S6 of this embodiment is:

[0164] ,

[0165] in, and are the dual variables of wind turbine i at the n+1th and nth iterations respectively. , is the penalty factor, is the set of feeders, is the sum of the binary variables of all outgoing lines of wind turbine i on feeder f at the nth iteration, For all wind turbines on feeder f; when determining whether the preset iteration end condition is met in step S7, the preset iteration end condition is that the number of iterations is equal to the preset threshold, and the residual of the original problem is equal to Less than the convergence judgment value ( ), or the residual of the original problem and the dual problem Less than the convergence judgment value ( ), where the original problem refers to the objective function of the total cost of feeder f, and the dual problem is the objective function obtained by removing the quadratic penalty term from the augmented Lagrangian function. The residual of the original problem is The calculation function expression is:

[0166] ,

[0167] in, is the residual of the original problem at the n+1th iteration, is the sum of the binary variables of all outgoing lines of wind turbine i on feeder f at the n+1th iteration; the residual of the original problem and the dual problem The calculation function expression is:

[0168] .

[0169] To verify the optimal economic planning method for the offshore wind farm power collection system in this embodiment, a simulation was performed. Table 1 lists the specifications of 33kV aluminum cross-linked polyethylene cables, including cross-sectional area, rated capacity, resistance per unit length, inductance, and cost.

[0170] Table 1: Specifications of 33kV aluminum cross-linked polyethylene cable

[0171]

[0172] In Table 1, MVA (Mega Volt Amperes) refers to the capacity of the cable in megavolt-amperes (million volt-amperes).

[0173] To quantify the technical effectiveness of the method of this embodiment, the following methods were compared: a radial topology design based on mathematical programming and a ring topology design. Mathematical programming guaranteed the global optimal solution for this topology. The offshore wind farm with 30 turbines had a 5MW turbine load, a failure rate of 0.02 per kilometer-year, and an average repair time of 720 hours. The offshore wind farm with 42 turbines had a 6.25MW turbine load, a failure rate of 0.01 per kilometer-year, and an average repair time of 720 hours. The final results are shown in Table 2.

[0174] Table 2: Economic comparison of offshore wind farms using 30 / 42 wind turbines

[0175]

[0176] In Table 2, cable costs, power losses, expected unpowered energy costs, and total costs are all expressed in thousands of US dollars (k$). As shown in Table 2, compared to a radial topology design, the cable cost savings of this embodiment for systems with 30 and 42 wind turbines are 8.25% and 19.21%, respectively. Compared to a ring topology design, the cable cost savings of this embodiment for systems with 30 and 42 wind turbines are 3.37% and 1.15%, respectively.

[0177] Figure 2: The annual average output power curves of the two offshore wind farms in this embodiment, (a) is the annual average output power curve of the offshore wind farm equipped with 30 wind turbines, and (b) is the annual average output power curve of the offshore wind farm equipped with 42 wind turbines.

[0178] Figure 3 This is a comparison of the optimal topological structures obtained by different methods for an offshore wind farm power collection system equipped with 30 wind turbines in an embodiment of the present invention. Figure 4 The following is a comparison of the optimal topological structures of the offshore wind farm collection system equipped with 42 wind turbines in this embodiment obtained by different methods, where (a) is the radial topology obtained based on the mathematical programming method, (b) is the ring topology obtained based on the mathematical programming method, and (c) is the heterogeneous topology obtained based on the method of this embodiment. Figure 3 and Figure 4 The feasibility of the economic optimization planning method of the offshore wind farm collection system in this embodiment is proved.

[0179] Figure 5 Figure 1 shows the curves between the number of iterations and the total cost for the two offshore wind farms in this example, with the total cost expressed in millions of US dollars (M$). (a) shows the curve between the number of iterations and the total cost for the offshore wind farm with 30 wind turbines, and (b) shows the curve between the number of iterations and the total cost for the offshore wind farm with 42 wind turbines. The curves between the number of iterations and the total cost indicate an overall downward trend in cost during the iterations. The preset end-of-iteration conditions were triggered at the 9th and 32nd iterations for the offshore wind farms with 30 and 42 wind turbines, respectively. Although the total costs of the 30-turbine offshore wind farm were lower than the final converged total cost at the 5th and 8th iterations, the wind turbines were not connected to the topological network, thus failing to meet the convergence criteria. The 9th iteration, when the preset end-of-iteration condition was triggered, achieved the lowest cost and no wind turbine connection issues existed, thus triggering the preset end-of-iteration condition.

[0180] In addition, this embodiment also provides an offshore wind farm collection system economic optimization planning system, including an interconnected microprocessor and memory, the microprocessor being programmed or configured to execute the offshore wind farm collection system economic optimization planning method. In addition, this embodiment also provides a computer-readable storage medium, the computer-readable storage medium storing a computer program or instructions, the computer program or instructions being programmed or configured to execute the offshore wind farm collection system economic optimization planning method via a processor. In addition, this embodiment also provides a computer program product, including a computer program or instructions, the computer program or instructions being programmed or configured to execute the offshore wind farm collection system economic optimization planning method via a processor.

[0181] Those skilled in the art should understand that the technical solution provided by the present invention may be in the form of a method, a system, or a computer program product. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-readable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The present invention is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present invention. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of processes and / or boxes in the flowchart and / or block diagram, may be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the functions described in the process. Figure 1 a process or multiple processes and / or boxes Figure 1 These computer program instructions can also be stored in a computer-readable memory that can guide a computer or other programmable data processing device to work in a specific way, so that the instructions stored in the computer-readable memory produce a product including the instruction device, which implements the function specified in the process. Figure 1 a process or multiple processes and / or boxes Figure 1 These computer program instructions can also be loaded onto a computer or other programmable data processing device, so that a series of operation steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process in the process. Figure 1 a process or multiple processes and / or boxes Figure 1 The steps for the function specified in one or more boxes.

[0182] The above description is merely a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiment. All technical solutions based on the concept of the present invention are within the scope of protection of the present invention. It should be noted that for those skilled in the art, various improvements and modifications that do not depart from the principles of the present invention should also be considered within the scope of protection of the present invention.

Claims

1. A method for economic optimization planning of an offshore wind farm collection system, characterized in that: The steps include: S1, obtain wind farm data of offshore wind farms; S2, based on the wind farm data of the offshore wind farm, construct the objective functions of cable cost, power loss and expected ungenerated energy cost for the collection system respectively, and add them together to obtain the objective function of the total cost; S3, based on the total cost objective function, an augmented Lagrangian function is constructed as a new objective function. The wind turbines of the offshore wind farm are initially divided into a single feeder. The new objective function is decomposed into multiple feeder sub-problems based on the alternating direction multiplier method. S4, considers the collection system as a heterogeneous topology consisting of radial cables and ring cables, and adds heterogeneous topology constraints to each feeder subproblem; S5, using the solver to obtain the optimal topology and total cost of each feeder subproblem; S6, update the dual variables in the augmented Lagrangian function; S7, judging whether the preset iteration end condition is met, if not, skipping to step S3; Otherwise, the optimal topology and total cost corresponding to each feeder of the collection system are output; Step S3 includes: S3.1, based on the objective function of the total cost, construct the Lagrangian function of the objective function shown in the following formula: ， in, is the Lagrangian function of the objective function, is the objective function of the total cost, For the fan assembly, is the dual variable of wind turbine i, Radial network The binary variable of the cable between wind turbine i and wind turbine j, the binary variable takes the value of 1 or 0 to indicate whether the cable is disconnected, the radial network A unidirectionally connected radial network formed by removing a "broken line" in a heterogeneous topology consisting of radial cables and ring cables. The "broken line" refers to the outgoing line of the root node of the ring cable. S3.2, based on the Lagrangian function of the objective function, an augmented Lagrangian function is constructed as the new objective function: ， in, is the augmented Lagrangian function, is the penalty factor; S3.3, initially divide the wind turbines in the offshore wind farm into a single feeder. Based on the alternating direction multiplier method, the new objective function is decomposed into multiple feeder subproblems. The function expression of the feeder subproblem for any feeder f is obtained as follows: ， ， ， in, is the feeder subproblem for any feeder f, is the objective function of the total cost of feeder f, is a three-dimensional variable matrix The part of the feeder f, is a three-dimensional variable matrix The part of the feeder f, For all wind turbines on feeder f, is the dual variable of wind turbine i on feeder f, is the sum of the binary variables of all outgoing lines of wind turbine i on feeder f, Radial network The binary variable of the cable between wind turbine i and wind turbine j on feeder f, is the sum of the binary variables of all outgoing lines of wind turbine i except the wind turbine on feeder f, For offshore wind farms, except for wind turbines on feeder f, Radial network The binary variable of the cable between wind turbines i and j on feeder f is removed from the equation. The binary variable takes the value 1 or 0 to indicate whether the cable is disconnected.

2. The economic optimization planning method for offshore wind farm power collection system according to claim 1 is characterized in that: The functional expression of the objective function of cable cost, power loss and expected ungenerated energy cost constructed in step S2 is: ， ， ， in, is the objective function of cable cost, is the objective function of power loss, is the objective function of the expected cost of ungenerated electricity, is the three-dimensional variable matrix of the radial cable, the three-dimensional variable matrix Elements in is the binary sorting variable of the cable between wind turbines i and j when the maximum sorting position is p, is the three-dimensional variable matrix of the ring cable, the three-dimensional variable matrix Elements in is the binary sorting variable of the cable between wind turbines i and j when the maximum sorting position is q. The binary sorting variable takes the value of 1 or 0 to indicate whether the corresponding cable is built. and are the cost and resistance of the cable between fans i and j in the radial cable section when the maximum sorting position is p, and are the cost and resistance of the cable between fans i and j in the ring cable when the maximum sorting position is q, is the length of the cable between fans i and j, For cable assembly, is a set of bidirectional sequence positions of the cable, including positive and negative sequence positions. The maximum sequence position in the radial portion of the cable is equal to the cable sequence position, and the maximum sequence position in the annular portion of the cable is the larger value of the positive and negative sequence positions. The cables between fans i and j in the radial part of the cable are arranged in the center. The power flowing under normal operating conditions is The cable between fans i and j in the ring cable is in the center sorting position The power flowing under normal operating conditions, the center sorting position of the radial part cable Equal to the maximum sorting position, the center sorting position of the ring section cable is equal to the average of the positive and negative sort positions, is the mean time to repair a cable fault, is the cable failure rate, This is the radial portion of the cable.

3. The economic optimization planning method for offshore wind farm power collection system according to claim 1 is characterized in that: When adding heterogeneous topology constraints to each feeder sub-problem in step S4, the heterogeneous topology constraints include heterogeneous topology feeder constraints, ring constraints on the heterogeneous topology, and radial network constraints after "broken lines" are removed on the heterogeneous topology. The radial network constraints after "broken lines" are removed on the heterogeneous topology include radial network constraints after forward "broken lines" are removed and radial network constraints after reverse "broken lines" are removed.

4. The economic optimization planning method for offshore wind farm power collection system according to claim 3 is characterized in that: The feeder constraints of the heterogeneous topology include: (1) there is at most one incoming line at the transformer node, and at most one feeder at each feeder subproblem; (2) the outgoing lines of all wind turbine nodes are 0-2 to limit a feeder to at most one ring; (3) the transformer node is the root node; (4) the wind turbine node with an outgoing line equal to 2 is the root node; (5) the wind turbine node with an outgoing line less than or equal to 1 is a non-root node; the ring constraints on the heterogeneous topology include: (6) the ring is part of the original feeder; (7) the outgoing lines of all nodes on the ring are equal to the incoming lines; (8) the outgoing lines of the transformer node on the ring are equal to the outgoing lines of the transformer node of the original feeder; (9) the outgoing lines of other root nodes on the ring are equal to the outgoing lines of other root nodes of the original feeder minus 1; (10) the radial part and the ring part constitute the feeder; (11) a cable on the radial part can only correspond to one maximum sequence position; (12) a cable on the ring part can only correspond to one maximum sequence position.

5. The economic optimization planning method for offshore wind farm power collection system according to claim 3 is characterized in that: The radial network constraints after the forward "break" is removed include: (13) the "break" in the forward direction must be on the ring; (14) the "break" in the forward direction can only be the outgoing line of the root node; (15) the radial feeder formed after the "break" in the forward direction is removed; (16) the forward power flow of the radial topology is conserved; (17) each cable occupies exactly one positive sorting position in the forward direction; (18) in the radial network in the forward direction, the number of outgoing lines of the wind turbine node does not exceed one; constraints (16) to (18) are used to ensure that a unidirectionally connected radial network is formed after the "break" is removed in the forward direction; the radial network constraints after the reverse "break" is removed include: (19) the ring of the feeder f in the forward direction is transposed to obtain The ring part in the reverse direction; (20) The radial network formed after removing the "broken line" in the reverse direction is equal to the original network minus the ring in the forward direction plus the ring in the reverse direction minus the "broken line" in the reverse direction; (21) The "broken line" in the reverse direction must be on the ring; (22) The "broken line" in the reverse direction can only be the outgoing line of the root node; (23) The radial feeder formed after removing the "broken line" in the reverse direction; (24) The reverse power flow of the radial topology is conserved; (25) Each cable occupies exactly one positive sorting position in the reverse direction; (26) In the radial network in the reverse direction, the number of outgoing lines of the wind turbine node does not exceed one; Among them, constraints (24) to (26) are used to ensure that a unidirectionally connected radial network is formed after removing the "broken line" in the reverse direction.

6. The economic optimization planning method for offshore wind farm power collection system according to claim 1, characterized in that: The function expression for updating the dual variable in the augmented Lagrangian function in step S6 is: ， in, and are the dual variables of wind turbine i at the n+1th and nth iterations respectively. , is the penalty factor, is the set of feeders, is the sum of the binary variables of all outgoing lines of wind turbine i on feeder f at the nth iteration, For all wind turbines on feeder f; when determining whether the preset iteration end condition is met in step S7, the preset iteration end condition is that the number of iterations is equal to the preset threshold, and the residual of the original problem is equal to Less than the convergence judgment value , or the residual of the original problem and the dual problem Less than the convergence judgment value , where the original problem refers to the objective function of the total cost of feeder f, and the dual problem is the objective function obtained by removing the quadratic penalty term from the augmented Lagrangian function. The residual of the original problem is The calculation function expression is: ， in, is the residual of the original problem at the n+1th iteration, is the sum of the binary variables of all outgoing lines of wind turbine i on feeder f at the n+1th iteration; the residual of the original problem and the dual problem The calculation function expression is: 。 7. An economic optimization planning system for an offshore wind farm power collection system, comprising a microprocessor and a memory connected to each other, characterized in that: The microprocessor is programmed or configured to execute the economic optimization planning method for an offshore wind farm collection system according to any one of claims 1 to 6.

8. A computer-readable storage medium having a computer program or instruction stored therein, characterized in that: The computer program or instruction is programmed or configured to execute the economic optimization planning method for an offshore wind farm collection system according to any one of claims 1 to 6 through a processor.

9. A computer program product comprising a computer program or instructions, characterized in that The computer program or instruction is programmed or configured to execute the economic optimization planning method for an offshore wind farm collection system according to any one of claims 1 to 6 through a processor.

Images