Method for power optimization of offshore wind power system based on dynamic regional relaxation
By employing a dynamic regional convex relaxation method, the nonlinearity and nonconvexity of the power flow optimization problem in offshore wind power systems are addressed, achieving an efficient and feasible global optimal solution and optimizing the energy management of offshore wind power systems.
Patent Information
- Application Number
- CN202210058637.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-01-19
- Publication Date
- 2025-11-25
- Estimated Expiration
- 2042-01-19
AI Technical Summary
Existing technologies are insufficient for efficiently solving the power flow optimization problem of offshore wind power systems, and it is difficult to guarantee the global optimality of the optimization solution. Common convex relaxation methods cannot obtain feasible optimal solutions when information is lost or the topology changes.
The dynamic domain convex relaxation method is adopted. By establishing the original optimization model of the offshore wind power system, relaxation variables are introduced, the solution domain is dynamically reconstructed and shrunk, and the McCormick convex hull is used for relaxation, which is transformed into a convex optimization problem and solved by the interior point method.
It achieves efficient optimization solutions for offshore wind power systems, ensuring the feasibility and global optimality of the solution, reducing the gaps in the relaxation domain, and improving the efficiency and convergence performance of the solution.
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Figure CN114447933B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The application belongs to the field of power systems, and particularly relates to an energy optimization method for an offshore wind power system based on a dynamic convex hull relaxation method. BACKGROUND
[0002] With the steady progress of energy reform worldwide, the proportion of renewable energy such as wind energy and solar energy in the energy supply composition is increasing year by year. At the end of 2019, China's wind power installed capacity was 210 million kilowatts, accounting for 11% of the total power installed capacity. It is predicted that by 2035, the wind power installed capacity will exceed 1 billion kilowatts, of which 250-350 million kilowatts will be offshore wind power. Wind power will become one of the main power sources that affect China's energy pattern and ensure energy security. At the same time, considering various loads such as offshore oil and gas platforms and the development direction of offshore wind power system networking, it is very important to manage and optimize the energy of offshore wind power systems.
[0003] Similar to onshore power systems, offshore wind power systems are typical nonlinear systems. When energy management is performed, how to reduce the loss of the system is the top priority of optimization. The loss of offshore wind power is usually caused by line loss during transmission of the submarine cable. Therefore, it is of great significance to propose an effective solution to reduce line loss for fine physical modeling of offshore wind power systems, while ensuring energy conservation and meeting the corresponding physical relationship.
[0004] In solving related optimization problems of nonlinear programming, since the problem is NP-hard, common analytical solutions are difficult to solve efficiently. Some heuristic algorithms often require a large amount of running time and storage space when searching for solutions, and it is difficult to ensure that the global optimal solution is found. On the contrary, if an optimization problem is a convex optimization problem, it can be efficiently and quickly solved to the global optimal solution by analytical methods. Therefore, if a certain convex relaxation method is used to reshape the solution domain of non-convex nonlinear problems and find the optimal solution on the relaxed boundary, both efficient solution and global optimal solution can be achieved.
[0005] In the current research on energy optimization of offshore wind farms, algorithms using convex relaxation means are still relatively few. At the same time, common convex relaxation methods will relax variables by variable substitution, which will cause some information loss. Thus, it is difficult to recover the complete system information before relaxation from the optimal solution after relaxation, and it is difficult to obtain a feasible optimal solution. Some specific relaxation recovery methods under certain conditions are often proposed in the existing literature, so that the proposed conditions cannot be met due to changes in the topology structure and system parameters, and thus the universality is poor. Therefore, how to use convex relaxation methods to achieve accurate convex relaxation of optimization and optimize the solution of offshore wind power systems has important significance and a wide range of applications. SUMMARY
[0006] The application aims to overcome the problem that the existing solution method cannot efficiently solve the power flow optimization problem of the offshore wind power system and it is difficult to ensure the global optimality of the optimization solution, and provides an optimization modeling and solving method based on dynamic region convex relaxation.
[0007] In order to achieve the above application purpose, the method adopts the following technical scheme:
[0008] An optimization method for dynamic convex relaxation of offshore wind power system, characterized in that it comprises: establishment of an original optimization model of offshore wind power system, construction of a variable relaxation model, reconstruction and contraction of a dynamic region, and solution of an optimization problem.
[0009] I. Establishing an original optimization model of offshore wind power system
[0010] Specifically, it can be divided into the following three steps:
[0011] 1.1 Determining the adjustable variables and physical constraint constants in the offshore wind power system
[0012] 1.2 Establishing an optimization objective function expression
[0013] 1.3 Establishing power system constraints based on offshore wind power system operating conditions
[0014] II. Establishing a variable relaxation model
[0015] Specifically, it involves introducing and defining relevant relaxation variables:
[0016] In the offshore wind power system, define the variable W ii , W ij respectively representing the square term of the voltage variable U i of node i and the voltage product of adjacent node voltage variable U i and U j ; the mathematical expression is:
[0017]
[0018] U i U j = W ij .
[0019] At the same time, define the square variable l ij of line current I ij , and define the square variable SS ij of S ij . Then,
[0020]
[0021] S ij +S ji =Z ij l ij ,
[0022]
[0023] SS ij =W ii l ij .
[0024] where Z ij is the line impedance, S ij and S ji are the complex power from node i to node j and from node j to node i, respectively.
[0025] At the same time, according to the definition of the slack variable, and the upper and lower bounds of the related variables, the upper and lower bounds of the slack variable can be confirmed.
[0026] Three, the reconstruction and contraction of dynamic region;
[0027] The process is mainly based on the variable characteristics, the solving region is reconstructed, and the solving domain constructed by all constraints becomes a convex set; at the same time, by changing the range of the variable, the excessive relaxation region is reduced, so as to ensure the effectiveness of the relaxation and the feasibility of the solution.
[0028] Wherein, the dynamic region reconstruction is specifically:
[0029] In the above step two of the variable relaxation, it can be known that the non-convex terms exist in the quadratic square term and the quadratic relaxation term. Therefore, for the equation constraint such as y=x 2 and z=xy, convex hulls are established respectively, and dynamic solving domain reconstruction is carried out. Among them, Figure 1 is a convex hull diagram. Specifically, for y=x 2 , by defining the upper and lower bounds of the variable x, and the two tangent lines based on the range of the variable x, the curve y=x 2 can be relaxed into a convex region. Similarly, for the surface z=xy, the range of the variable x and the variable y, and the tangent surface composed of the variable range can be relaxed. When the variable range in the figure changes, the size of the relaxation region changes, and the slope of the tangent and the tangent surface also changes accordingly. For y=x 2 , by defining the upper and lower bounds of the variable x, and the two tangent lines based on the range of the variable x, the curve y=x 2Relax to a convex region. Similarly, for the surface of z = xy, the relaxation can be performed by the variable x and the variable y, and by the tangent plane formed by the variable range. When the variable range changes in the figure, the size of the relaxation region changes accordingly, and the slope of the tangent and the tangent plane also changes accordingly. Therefore, the non-convex inequality relationship in step two can be written as:
[0030]
[0031]
[0032]
[0033]
[0034]
[0035]
[0036] In the formula, the upper subscripts min and max represent the lower limit and the upper limit of the variable, respectively; W ii , W ij , l ij , SS ij is the relaxation variable defined in step (2); β i , β ij , β li , β si , β slij is the variable defining the size of the convex hull; U i , U j is the voltage variable of node i and node j; I ij , S ij is the current flowing through the line i-j and the apparent power.
[0037] The above constraints are obtained by relaxing the non-convex equality constraints in step two. In order to narrow the relaxation region to ensure the feasibility of the solution, the following tightening process is proposed:
[0038] The above equality constraints can be arranged in the following vector form:
[0039] A[U i , U j , I ij , S ij ] T = B[W ii , W ij , l ij , SS ij ] T + β
[0040] In the formula, A and B are matrices with constant coefficients, T represents the rank transformation operator, and β represents the vector composed of all the aforementioned β values. In this vector form operation, it can be observed that according to [W... ii W ij , l ij SS ij The range of variables [U], the signs of A and B, and the range of β can determine the range of variables [U]. i U j I ij S ij The range of [U]. i U j I ij S ij When the range of [U] changes, the coefficients of the constant real number matrices A and B also change accordingly. This process repeats itself, when [U]... i U j I ij S ij The contraction process ends when the range of the variable [ ] no longer changes.
[0041] To ensure the effectiveness of the contraction process, a determination of the objective function is introduced as a boundary condition. The optimal solutions of the objective function before relaxation and after contraction are denoted as f, respectively. obj With f′ obj Therefore, during each iteration of contraction, the value of the objective function f should be the value of the objective function after the previous iteration [f]. obj f obj Within the range of '].
[0042] IV. Optimizing the problem-solving process;
[0043] Using the bounds of the compressed variables as the final range of system variables, the quadratic constraints are transformed into convex hull constraints, and the optimization problem is solved again. The specific transformation form of the quadratic constraints is: transforming constraints of the form y = x... 2 Relaxation is performed using the McCormick convex hull.
[0044] x 2 ≤y,
[0045] y≤(x max +x min )xx max x min .
[0046] The quadratic constraint of the form z = xy is relaxed using the McCormick convex hull.
[0047] z≤x min y+y max xx min y max ,
[0048] z ≤ x max y + y min x - x max y min ,
[0049] z ≥ x min y + y min x - x min x min ,
[0050] z ≥ x max y + y max x - x max x max .
[0051] Thus, the constraints on the slack variables in step (2) are relaxed by convex hull relaxation to,
[0052]
[0053]
[0054]
[0055]
[0056]
[0057]
[0058] SS ij ≤ W ii min l ij + l ij max W ii - W ii min l ij max
[0059] SS ij ≤ W ii max l ij + l ij min W ii - W ii max l ij min
[0060] SS ij ≥ W ii min l ij + lij min W ii -W ii min l ij min
[0061] SS ij ≥W ii max l ij +l ij max W ii -W ii max l ij max
[0062] W ij ≤U i min U j +U j max U i -U i min U j max
[0063] W ij ≤U i max U j +U j max U i -U i max U j min
[0064] W ij ≥U i min U j +U j min U i -U i max U j min
[0065] W ij ≥U i max U j +U j max U i -U i max U j max
[0066] After the convex hull relaxation, the power optimization problem of offshore wind power system becomes a convex optimization problem in a fixed convex set. The new variable range after the contraction in step (3) is written into the convex hull relaxation above, and the interior point method is used to solve the convex optimization problem after the convex hull relaxation to obtain the power solution of the optimized offshore wind power system.
[0067] The beneficial effects of the present application are:
[0068] By changing the feasible region, the nonlinearity and non-convexity of the offshore wind power optimization problem can be overcome. By dynamically shrinking the solution domain, the relaxation domain is effectively reduced, and the feasibility of the optimization solution is ensured. At the same time, by adding the value of the objective function before iteration as a limit when shrinking the feasible region, the effectiveness of each tightening is ensured. Compared with the existing method, the present method can quickly realize optimization solution with good convergence performance and ensure the feasibility of the solution. BRIEF DESCRIPTION OF DRAWINGS
[0069] Figure 1 The left graph is the solution domain remodeling method of y=x2, that is, the curve is surrounded by the shaded part of the graph; the right graph is the solution domain remodeling method of z=xy, that is, the surface is surrounded by the shaded part of the solid graph.
[0070] Figure 2 The simulation system is used to verify the effectiveness of the present application. The graph is the collection line wiring diagram of the offshore wind farm, and there are 63 wind turbines in the graph.
[0071] Figure 3 The horizontal axis represents the wind turbine output, and the vertical axis represents the total power on the grid. Figure 2 The horizontal axis represents the wind turbine output, and the vertical axis represents the total power on the grid. As can be seen from the graph, after power optimization, the wind turbine has more power on the grid under different wind turbine outputs.
[0072] Figure 4 The horizontal axis represents the wind turbine output, and the vertical axis represents the total power on the grid. As can be seen from the graph, after power optimization, the wind turbine has more power on the grid under different wind turbine outputs. Figure 2 The horizontal axis represents the iteration number, and the vertical axis represents the average gap of the convex hull relaxation. As can be seen from the graph, with iteration, the average relaxation gap gradually tends to 0. DETAILED DESCRIPTION
[0073] In order to more specifically describe the present application, the technical solutions of the present application will be described in detail below in combination with the drawings and specific implementation examples.
[0074] The optimization process of the present application mainly includes the above-mentioned optimization model establishment, variable relaxation model construction, dynamic region reconstruction and contraction, and optimization problem solving four main parts;
[0075] I. Establishing the initial optimization model for offshore wind power systems;
[0076] 1.1 Determine the dispatchable variables and physical constraint constants in the offshore wind power system;
[0077] In the modeling of offshore wind power systems, it is necessary to consider the voltage variable U at each node i in the power grid. i =V i ∠θ i The active power variable P generated by node i i g Reactive power variables Active power variable P of node i load i c Reactive power variables Establish equations relating equality and inequality; and simultaneously consider the variable current I flowing through line ij. ij Line admittance constant Y ij Conductivity constant G ij susceptance constant B ij The active power variable P flowing through line ij ij Reactive power variable Q ij and complex power variable S ij Equations are established for the variables between nodes. The optimization model of the power system mainly involves power flow constraints, energy constraints, voltage constraints, and output constraints of each load and generator; in addition, the network topology and wiring method of the power system also need to be considered.
[0078] 1.2 Establish an expression based on the optimization objective function;
[0079] The optimization objective of offshore wind farms is to maximize the amount of electricity fed into the grid, expressed as:
[0080] f = C E ∑P i g (1)
[0081] Among them, C E For wind power grid connection price, P i g Let be the active power of the wind turbine connected to the grid at node i, ∑ be the summation operation, and f be the objective function value.
[0082] 1.3 Based on the operating conditions of offshore wind power systems, establish power system constraints;
[0083] 1) In an offshore wind power system, the relationship between power, voltage, and current is as follows:
[0084]
[0085] Where * represents the conjugate operation, Sij , U i , I ij is a complex variable.
[0086] 2) The direct relationship between node voltage and current is
[0087] I ij = (U i -U j ) Y ij (3)
[0088] where Y ij is a complex variable.
[0089] 3) The active power and reactive power conservation relationship is
[0090]
[0091] where the superscript g represents the generation node, and the superscript c represents the load node. In the offshore wind power system, most of the wind turbine nodes are generation nodes, and there are few load nodes.
[0092] 4) Voltage node constraint
[0093]
[0094] where the superscripts min and max represent the lower and upper bounds of the variable, which are constants. Since Ui is a complex variable, the constraint indicates that the upper and lower bounds of the real part and the imaginary part are limited, respectively.
[0095] 5) Power constraint
[0096]
[0097] For the active power and the reactive power of the node, according to the operating constraints of the equipment, the upper and lower bounds thereof are limited. In the above formula, the active power and the reactive power are both real variables.
[0098] 6) Current constraint
[0099]
[0100] For the active power and the reactive power of the line, and the active power of the node, according to the operating constraints of the equipment, the upper and lower bounds thereof are limited. In the above formula, the active power and the reactive power are both real variables.
[0101] Through modeling, the mathematical expression of the optimization problem is:
[0102]
[0103] II. Establishment of variable relaxation model
[0104] In mathematical expression (7), the non-convex constraints of the optimization problem come from constraints (2) and (3). For this purpose, the slack variables W ii , W ij , l ij , SS ij are introduced and the constraints related to them are defined. Among them, the quadratic square term constraint is:
[0105]
[0106] The quadratic product term constraint is:
[0107]
[0108] By combining constraints (2) and (3) with the slack variables, we get:
[0109]
[0110] Due to the introduction of variable l ij , there are the following equality constraints:
[0111] S ij +S ji = Z ij l ij (12)
[0112] Correspondingly, the upper and lower bound constraints of the slack variables are
[0113]
[0114] The optimization problem after relaxation is
[0115]
[0116] In optimization problem (14), non-convex constraints exist in constraint (9) and constraint (10). Therefore, step three mainly improves these two equations.
[0117] III. Reconstruction and contraction of dynamic regions
[0118] In the region reconstruction, according to the method proposed for constraint (9), it can be written as constraint:
[0119]
[0120] For constraint (10), the above reconstruction method is:
[0121]
[0122] In the formula, the upper indexes min and max represent the lower bound and upper bound of the variable respectively; W ii , W ij , lij , SS ij is the slack variable defined in step (2); β i , β ij , β li , β si , β slij is the variable defining the size of the convex hull; U i , U j is the voltage variable of node i and node j; I ij , S ij is the current flowing on line i ~ j and the apparent power.
[0123] After the solution domain is reconstructed, the optimization problem (14) becomes
[0124]
[0125] In the area shrinkage, the above equation constraints (15), (16) are arranged, and the following vector form is formed:
[0126] A [U i , U j , I ij , S ij ] T = B [W ii , W ij , l ij , SS ij ] T + β
[0127] In the formula, A and B are constant number matrices, T represents the transpose operator, and β represents a vector composed of all β. In the vector form operation, it can be found that according to the variable range of [W ii , W ij , l ij , SS ij ], the positive and negative of A and B, and the range of β, the range of the variable [U i , U j , I ij , S ij ] can be determined. When the range of [U i , U j , I ij , S ij ] changes, the coefficients of the constant number matrices A and B also change. Follow this cycle, when the variable range of [U i , U j , I ij , S ij ] no longer changes, the shrinkage process ends.
[0128] In order to ensure the effectiveness of the shrinkage, the judgment of the objective function is introduced as a boundary condition in the shrinkage process. The optimization solutions of the objective function before and after the shrinkage are respectively denoted as f obj and f obj Therefore, in each iteration of the shrinkage, the value f of the objective function should be in the range of the value [f obj , f obj ] of the objective function after the last iteration.
[0129] Four, solving the optimization problem
[0130] According to the boundary of the variable after the shrinkage as the final value range of the system variable, the quadratic constraint is converted into a convex hull constraint, and the optimization problem is solved again. For the optimization problem (14), the non-convex constraints (9) and (10) are convexly relaxed. Among them, the constraint (9) will be converted into:
[0131]
[0132] The McCormick convex hull is used for relaxation, and the constraint (10) will become
[0133]
[0134] By using the variable range after the shrinkage, the interior point method is used to solve the relaxed convex optimization problem, and the optimization problem is in the form of:
[0135]
[0136] The final solution after optimization can be obtained. That is, the active power and reactive power distribution of each node when the wind power on-grid power is maximum is obtained.
[0137] Taking Figure 2 a wind farm system as an example, simulation test research is carried out. The system is a typical offshore wind farm, and there are 63 wind turbines. By using the above method, through the establishment of the original optimization model, the construction of the variable relaxation model, the reconstruction and shrinkage of the dynamic region, and the solution of the optimization problem, the simulation results shown in Figure 3 and Figure 4 are obtained. Figure 3 The optimization solution before and after the optimization is obtained, which shows the comparison of the active power on the system after the optimization under the condition that the output of the wind turbine is different. Figure 4 In the dynamic region reconstruction and shrinkage, the average gap of the convex hull is recorded in the iteration. Figure 4 It is shown that the average gap of the convex relaxation gradually decreases in the iteration process. In summary, by using the optimization method in the present application, the on-grid power of the wind power system can be effectively optimized; at the same time, the dynamic solution domain method proposed can effectively reduce the convex relaxation gap, thereby ensuring the feasibility of the optimization solution.
[0138] The foregoing description of the embodiments has been presented for the purpose of illustration and description. It is not intended to be exhaustive or to limit the application to the precise form disclosed. Modifications and variations are possible in light of the above teachings or can be acquired from practice of the application. As well, the application has been described above with the assistance of illustrative figures and detailed descriptions. It is obvious to a person skilled in the art that a variety of modifications and changes can be made without departing from the application disclosed in its broadest form.
Claims
1. A method for power optimization of an offshore wind power system based on dynamic zone relaxation, characterized by The following steps ； Step (1): establishing the original optimization model of the offshore wind power system; to establish the power system constraints; Step (2): based on the system original optimization model obtained in step (1), a variable relaxation model is established; specifically, related relaxation variables are introduced and defined: In an offshore wind power system, define variables W ii , W ij , respectively, representing the square term of the voltage variable U i of node i and the voltage product of adjacent node voltage variable U i and U j ; the mathematical expression is: U i U j = W ij . I defining the line current ij square variable l ij , defining S ij square variable of S is variable SS ij then, S ij +S ji =Z ij l ij , SS ij = W ii l ij . where Z is the line impedance, S is the line current, and P is the line power. ij where Z is the line impedance, S is the line current, and P is the line power. ij where Z is the line impedance, S is the line current, and P is the line power. ji where Z is the line impedance, S is the line current, and P is the line power. According to the definition of the relaxation variable and the upper and lower bounds of the related variables, the upper and lower bounds of the relaxation variable can be confirmed; Step (3): based on the optimization model and the relaxation variable in (1) and (2), the dynamic region is reconstructed and contracted, which is specifically according to the variable characteristics, the solving region is reconstructed, so that the solving domain constructed by all constraints becomes a convex set; at the same time, by changing the range of the variable, the excessive relaxation region is reduced, so as to ensure the effectiveness of the relaxation and the feasibility of the solution; Step (4): optimization problem solving: according to the boundary of the variable after reconstruction and contraction in step (3) as the final value range of the system variable, the quadratic constraint is converted into a convex hull constraint, and the optimization problem is solved again; the convex optimization problem after convex relaxation is solved by using the interior point method, and the power solution of the offshore wind power system after optimization is obtained; The step (3) includes dynamic reconstruction and range contraction of the region of the variable in the model; In the dynamic region reconstruction, the non-convex equation relationship in step (2) is specifically: where the upper indices min and max represent the lower and upper bounds of the variable, respectively; W ii , W ij , l ij , SS ij is the slack variable defined in step (2); β i , β ij , β li , β si , β slij is the variable defining the size of the convex hull; U i , U j is the voltage variable of node i and node j; I ij , S ij is the current flowing on line i~j and the apparent power; In the range contraction, the above equation constraint is arranged to form the following vector form: In the formula, A, B are constant matrix, T represents the transpose operator, representing the vector of all the above β composition; in the vector form operation, it can be found that according to the variable range of [W ii ,W ij , ij ,SS ij ] and the positive and negative of A, B and , the range of variable [U i ,U j ,I ij ,S ij ] can be determined; when the range of [U i ,U j ,I ij ,S ij ] changes, the coefficients of constant real matrix A, B also change accordingly; follow this back and forth, when the variable range of [U i ,U j ,I ij ,S ij ] no longer changes, the tightening process ends.
2. The dynamic zone relaxation based offshore wind power system power optimization method according to claim 1, characterized in that: The step (1) includes the following three steps: 1.1 determine the adjustable variable and the physical constraint constant in the offshore wind power system; 1.2 establish the optimization objective function expression; 1.3 based on the operating conditions of the offshore wind power system, establish the power system constraints.
3. The offshore wind power system power optimization method based on dynamic zone relaxation according to claim 1, characterized in that: In the range tightening process of step (3), the judgment of the objective function is introduced as a boundary condition; the optimization solution of the objective function before relaxation and after tightening are respectively recorded as f obj and f obj Therefore, in each iteration of tightening, the value f of the objective function should be in the range of the value of the objective function after the last iteration [f obj ,f obj ].
4. The dynamic zone relaxation based offshore wind power system power optimization method of claim 1, wherein: The step (4): according to the boundary of the tightened variable as the final value range of the system variable, the quadratic constraint is converted into a convex constraint, and the optimization problem is solved again; the specific conversion form of the quadratic constraint is: the form like y=x 2 The relaxation is carried out by using the McCormick convex hull, Wherein, x, y are variables; The quadratic constraint in the form of z=xy is relaxed by McCormick convex hull as z < x min y + y max x - x min y max , z < x max y + y min x - x max y min , z ≥ x min y + y min x - x min x min , z ≥ x max y + y max x - x max x max . Wherein, x, y, z are variables; Therefore, according to the definition of the relaxation variable in step (2), the related constraints of the relaxation variable are changed to SS ij ≤W ii min l ij +l ij max W ii -W ii min l ij max SS ij ≤W ii max l ij +l ij min W ii -W ii max l ij min SS ij ≥W ii min l ij +l ij min W ii -W ii min l ij min SS ij ≥W ii max l ij +l ij max W ii -W ii max l ij max W ij ≤U i min U j +U j max U i -U i min U j max W ij ≤U i max U j +U j min U i -U i max U j min W ij ≥U i min U j +U j min U i -U i min U j min W ij ≥U i max U j +U j max U i -U i max U j max After convex relaxation, the power optimization problem of the offshore wind power system becomes a convex optimization problem in a fixed convex set solving domain; write the new variable range contracted in step (3) into the above convex relaxation, and solve the convex optimization problem after convex relaxation by using the interior point method, so as to obtain the power solution of the offshore wind power system after optimization.