Semi-definite programming-based capacity matching method for network construction type converter and network following type converter

Abstract

The invention discloses a semi-definite programming-based capacity matching method for a network-constructing type converter and a network-following type converter, and the method comprises the following steps: S1, respectively building state space models of the network-constructing type converter and the network-following type converter, and constructing an overall state space model of a station comprising the network-constructing type converter and the network-following type converter through coordinate transformation; s2, describing a stability index by using semi-definite programming based on a Lyapunov equation, and deducing a stability sensitivity analytical expression of the ratio of the network-forming converter according to an original variable and a dual variable of the semi-definite programming; and S3, initializing the ratio of the network-building type converter, carrying out iteration by taking the stability sensitivity of the ratio of the network-building type converter as a gradient, and stopping until the target function value reaches a stability index limit value or the difference between target function values of two iterations is smaller than a convergence gap, thereby obtaining the optimal ratio of the network-building type converter. According to the method, the optimal network-constructing converter ratio can be accurately and quickly solved, and the stability and the economical efficiency of a new energy power generation system are ensured.

Description

Technical Field

[0001] The present invention relates to the technical field of operation control of new energy power generation systems, and particularly to a method for capacity ratio matching of grid-forming and grid-following converters based on semidefinite programming. Background Art

[0002] In new energy power generation systems, the control strategies for connecting new energy sources such as wind power and photovoltaic power to the AC grid through converters are divided into two categories: grid-following control and grid-forming control. Among them, grid-following control is the most widely used. Grid-following converters have good stability in strong grids with high short-circuit ratios. However, with the deepening of the "dual high" characteristics of the new power system, new energy gradually replaces traditional synchronous power sources, the grid strength decreases, and grid-following converters are prone to small-signal stability problems such as sub / supersynchronous oscillations.

[0003] By simulating the control method of a synchronous generator, the grid-forming converter exhibits dual characteristics with the grid-following converter and has good weak-grid adaptability. Existing research shows that the grid-forming converter exhibits a "positive resistance" characteristic in terms of circuit characteristics, which can weaken the negative damping characteristic introduced by the grid-following converter, thereby significantly improving the system oscillation damping and enhancing the system stability.

[0004] However, while grid-forming control improves stability, it sacrifices certain economy. On the one hand, the cost of grid-forming equipment is relatively high. On the other hand, its active support control requires reserved active power reserve, reducing the operating economy. Therefore, there is an urgent need for an accurate and fast method for optimizing the ratio of grid-forming converters to solve for the lowest ratio of grid-forming converters that meets the stability index. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for capacity ratio matching of grid-forming and grid-following converters based on semidefinite programming, which can accurately and quickly solve for the optimal ratio of grid-forming converters and ensure the stability and economy of new energy power generation systems.

[0006] To achieve the above purpose, the present invention provides a method for capacity ratio matching of grid-forming and grid-following converters based on semidefinite programming, including the following steps: S1. Respectively establish the state-space models of the grid-forming converter and the grid-following converter, and construct the overall state-space model of the station containing the grid-forming and grid-following converters through coordinate transformation; S2. Use semidefinite programming based on the Lyapunov equation to describe the stability index, and derive the analytical expression of the stability sensitivity of the grid-forming converter ratio according to the primal variables and dual variables of the semidefinite programming; S3. Initialize the ratio of the network-forming converters, and iterate with the stability sensitivity of the ratio of the network-forming converters as the gradient until the objective function value reaches the stability index limit value or the difference between the objective function values of two consecutive iterations is less than the convergence gap and then stop to obtain the optimal ratio of the network-forming converters.

[0007] Preferably, in S1, the wind-solar power station includes units of grid-following converters and units of grid-following converters, which are connected to the power grid through an equivalent impedance Z c ; The construction process of the overall state space model of the power station is as follows: The mathematical models of each control link and the filtering circuit of the grid-following converter are: ; In the formula, , are the phase angle and frequency obtained by the grid-following phase-locked loop respectively, , are the PI parameters of the phase-locked loop respectively, , are the PI parameters of the power outer loop respectively, , are the PI parameters of the current inner loop respectively, , are the active and reactive powers output by the converter respectively, represents the reference value, is the filtering inductor, , are the current and voltage at the filter outlet respectively, represents the reference value, is the voltage at the converter outlet.

[0008] Preferably, the mathematical models of each control link and the filtering circuit of the network-forming converter are: ; In the formula, is the frequency obtained by the network-forming virtual synchronous control, D , J are the damping coefficient and inertia of the virtual synchronous control loop respectively, E is the internal electromotive force obtained by the voltage droop control, is the voltage droop coefficient, k pv , k iv are the PI parameters of the voltage outer loop respectively, k pc , k ic are the PI parameters of the current inner loop respectively,P , Q are the active and reactive power output of the converter respectively. represents the reference value, L f is the filter inductor, , are the filter outlet current and voltage respectively, represents the reference value, is the converter output voltage.

[0009] Preferably, the mathematical models of the grid-type converter, the grid-forming converter and the AC network are combined by coordinate transformation, and linearized at the equilibrium point to obtain the overall state space model of the station: ; In the formula, is the system state variable, the matrix A is the system state matrix, the small signal stability of the system is related to the matrix A is related to the eigenvalues ​​of .

[0010] Preferably, in S2, the Lyapunov equation is used to describe the stability of the system. The second Lyapunov method states that if and only if there exists a real symmetric positive definite matrix satisfy , the system is asymptotically stable, and the related Lyapunov function is , is any given negative real number; The stability index is further designed as the solution to the following semidefinite programming problem: ; The Lyapunov equation requires , so set a constant that tends to 0 Make , which is consistent with is equivalent to setting , if the system is stable, the stability index obtained by semidefinite programming is will be negative; Stability index The absolute value of is the lower limit of the convergence speed after perturbation, and from the above semidefinite programming problem: ; Define an analytical formula for accurately calculating stability sensitivity, and derive the sensitivity of Jacobian matrix elements from the convexity of semidefinite programming The analytical expression of the stability sensitivity is obtained by using the chain rule. .

[0011] Preferably, the stability sensitivity is derived as follows: First, convert the original form of the above semidefinite programming problem into the standard form: ; where , the vector includes the stability index and the lower triangular elements of the symmetric matrix , , , ; considering all the constraints in the original semidefinite programming, define , where , , represents the set of all n -dimensional real symmetric matrices; corresponding to the constraints in the aforementioned original semidefinite programming, , , , , , , , , , represents the basis of the n -dimensional symmetric matrix, ; Secondly, write out the standard form of the dual problem of the above standard form of the semidefinite programming problem: ; where, the symmetric matrix Z represents the dual variable of the original variable ; Then, according to the Slater condition, there exists a strictly feasible solution of the primal problem, such that , and at the same time there exists a strictly feasible solution of the dual problem, satisfying and , ; this condition guarantees the strong duality of the semidefinite programming problem, and the duality gap at the optimal value is 0: ; and because and , we get: ; Since the proposed semidefinite programming problem is based on matrix inequalities while the standard convex problem is based on scalar inequalities, to conveniently derive the parameter sensitivity using dual variables, the "svec" calculation is introduced to vectorize the matrices in the semidefinite programming problem, obtaining a standard convex optimization form. Then, the parameter sensitivity formula for the semidefinite programming problem is established in the way of traditional convex problems. To facilitate representation and matrix operations, the function "svec" is defined as follows: mapping to , ; Then, the relationship between matrix and vector calculations is established through the "svec" function and the inner product: ; ; Let , then the above formula can be expressed as: ; Since the duality gap is 0, we have: ; The symmetric Kronecker product is used to simplify the expression. Its definition is that for any -dimensional symmetric matrix X , there exists M , N ∈ such that: ; Therefore can be expressed as: ; Then, by combining and , the function G is defined as: ; where , at the optimal value of the given parameter ; Substantially, is regarded as a variant of the KKT conditions under matrix inequalities. Since G and c are both continuously differentiable, the derivative of the function is expressed as: are both continuously differentiable, the derivative of the function is expressed as: ; At the optimal value , it is nonsingular. The calculation formula for the parameter sensitivity is: ; where the derivative Expressed as: ; The first element of the vector is the stability index , and for the sake of concise expression, a vector containing is defined. Therefore, the stability index is also the first element; Finally, by applying the chain rule of differentiation, the sensitivity of the stability index to the controllable variable, i.e., the ratio of the network-forming converters, is obtained: ; where is the partial derivative of the Jacobian matrix element containing with respect to

[0012] Preferably, in S3, the ratio of the network-forming converters is initialized to the upper limit of the ratio of the network-forming converters at the substation , and the limit value of the stability index is set to . The optimization algorithm process is as follows: S31. Set the initial value of the ratio parameter of the network-forming converters participating in the optimization , and let ; S32. Calculate the objective function value and the stability sensitivity according to the method in step S2; S33. Judge the termination condition; S34. Iteratively update the ratio of the network-forming converters : ; where is the iteration step size. Substitute the updated into step S32, and let .

[0013] Preferably, in S33, specifically: Termination condition 1: When , the difference between the objective function values of two iterations satisfies the convergence gap ε, i.e.: ; Termination condition 2: When the stability index is within the range of the limit value , i.e.: ; The algorithm stops and outputs the optimized result when any termination condition is met. If none of the termination conditions are satisfied, it proceeds to step S34 to iteratively update the matching parameters of the network-forming converter.

[0014] Therefore, by adopting the above method for matching the capacities of the network-forming and grid-following converters based on semidefinite programming, the present invention can analytically obtain the stability sensitivity by utilizing the strong duality of semidefinite programming, and further iteratively obtain the optimal matching of the network-forming converter, avoiding the process of approximately solving the sensitivity through multiple optimization solutions in the traditional numerical perturbation method, significantly improving the calculation efficiency and accuracy, achieving accurate and rapid solution of the optimal matching of the network-forming converter, and ensuring the stability and economy of the new energy power generation system.

[0015] Next, through the attached drawings and embodiments, the technical solution of the present invention will be further described in detail. Description of the Drawings

[0016] Figure 1 It is a flowchart of an embodiment of the method for matching the capacities of the network-forming and grid-following converters based on semidefinite programming of the present invention; Figure 2 It is a schematic diagram of the topology of the wind-solar power station and the network-forming control mode targeted by the present invention; Figure 3 It is a schematic diagram of the principle for constructing the overall state space model of the power station of the present invention; Figure 4 It is a flowchart of the optimization algorithm for the matching of the network-forming converter of the present invention; Figure 5 It is a comparison diagram of the errors between the stability sensitivity analysis method and the numerical perturbation method in the present invention; Figure 6 It is a validation diagram of the effectiveness of the method for matching the capacities of the network-forming and grid-following converters based on semidefinite programming of the present invention. Detailed Embodiments

[0017] The technical solution of the present invention will be further described below through the attached drawings and embodiments.

[0018] Unless otherwise defined, the technical terms or scientific terms used in this invention shall have the ordinary meanings as understood by those of ordinary skill in the field to which this invention pertains. The "first", "second" and similar terms used in this invention do not denote any order, quantity or importance, but are only used to distinguish different components. Words such as "comprising" or "including" mean that the elements or objects appearing before this word cover the elements or objects listed after this word and their equivalents, without excluding other elements or objects. Words such as "connected" or "coupled" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Upper", "lower", "left", "right", etc. are only used to represent relative positional relationships, and when the absolute position of the object being described changes, the relative positional relationship may also change accordingly.

[0019] Matrix inequality symbols are used in linear algebra and matrix analysis to represent specific relationships between matrices. Among them, A 0 indicates that matrix A is a positive definite matrix, and A 0 indicates that matrix A is a semi - positive definite matrix, and A B indicates that A - B is a semi - negative definite matrix.

[0020] Embodiment 1 As Figure 1 shown, the present invention provides a method for capacity ratio matching of grid - forming and grid - following converters based on semidefinite programming, including the following steps: S1. Respectively establish the state - space models of the grid - forming converter and the grid - following converter, and construct the overall state - space model of the substation containing the grid - forming and grid - following converters through coordinate transformation.

[0021] The topology of the wind - solar substation and the grid - forming control mode are as Figure 2 shown. The wind - solar substation includes units of grid - following converters and units of grid - following converters, which are connected to the power grid through the equivalent impedance Z c ; The process of constructing the overall state - space model of the substation is as follows: The mathematical models of each control link and the filtering circuit of the grid - following converter are: ; In the formula, , are respectively the phase angle and frequency obtained by the grid - following phase - locked loop, , are respectively the PI parameters of the phase - locked loop, , are respectively the PI parameters of the power outer loop, , They are the current inner loop PI parameters, , are the active and reactive power output of the converter respectively ( ref represents reference value), is the filter inductor, , They are the filter outlet current and voltage ( represents reference value), is the converter output voltage.

[0022] The mathematical models of each control link and filter circuit of the grid-type converter are as follows: ; In the formula, The frequency obtained for network-based virtual synchronous control is D , J are the damping coefficient and inertia of the virtual synchronous control loop, E is the internal potential obtained by voltage droop control, k Q is the voltage droop coefficient, k pv , k iv They are the voltage outer loop PI parameters, k pc , k ic They are the current inner loop PI parameters, P , Q are the active and reactive power output of the converter respectively ( ref represents reference value), L f is the filter inductor, i odq , u odq They are the filter outlet current and voltage ( represents reference value), u idq is the converter output voltage.

[0023] For the above system, according to Figure 3 The modeling method is to combine the mathematical models of the grid-type converter, the grid-type converter and the AC network through coordinate transformation, and linearize them at the equilibrium point, so that the overall state space model of the station can be obtained as follows: ;

[0024] In the formula, is the system state variable, the matrix A is the system state matrix, the small signal stability of the system is related to the matrix A is related to the eigenvalues ​​of .

[0025] S2. Use semidefinite programming based on Lyapunov equation to describe the stability index, and derive the analytical expression of the stability sensitivity of the network-forming converter ratio according to the primal variables and dual variables of the semidefinite programming.

[0026] Use the Lyapunov equation to describe the system stability. The second Lyapunov method points out that when and only when there exists a real symmetric positive definite matrix satisfies , the system has asymptotic stability, and the relevant Lyapunov function is , where

[0027] is an arbitrarily given negative real number. ;

[0028] The Lyapunov equation requires , so a constant tending to 0 is set such that , which is equivalent to . At the same time, such a transformation makes the feasible region change from an open set to a closed set, ensuring the existence of extreme points in the feasible region. In addition, to prevent the objective function value of this problem from being negative infinity, is set. If the system is stable, the stability index obtained by the semidefinite programming will be negative.

[0029] The absolute value of the stability index is the lower limit of the convergence speed after perturbation, because from the above semidefinite programming problem, it can be obtained that: ;

[0030] The method based on the Lyapunov function provides an overall evaluation of the stability, that is, whether the system is stable and the magnitude of the convergence speed. In this embodiment, the stability index based on the Lyapunov function is selected because this index is more operable. Different from the eigenvalue analysis, the stability index is given by a convex semidefinite programming problem, which has strong duality. In this embodiment, an efficient method is designed to calculate the stability sensitivity using its strong duality, which greatly reduces the computational burden on the premise of ensuring analytical accuracy. This method is applicable to stability judgment and convergence speed evaluation, while the study of oscillation modes is not within the scope of discussion.

[0031] The stability constraint can be described as: , ​is a controllable variable that can be used to enhance the stability index. In this embodiment represents the capacity ratio of the grid-forming converter represents the limit value of the stability index. To make the stability index meet the constraints, it is necessary to appropriately adjust by calculating the corresponding sensitivity However, since and the functional relationship of is implicit, it is very difficult to obtain the sensitivity. The mainstream sensitivity analysis method is the numerical perturbation method. The estimation method for the stability sensitivity of is as follows: ;

[0032] However, the estimation result strongly depends on the value of the perturbation Therefore, the numerical perturbation method is inaccurate, and since the stability index needs to be calculated twice to obtain the sensitivity of a single variable its computational burden is very high.

[0033] In this embodiment, an analytical formula for accurately calculating the stability sensitivity is defined. Starting from the convexity of the semidefinite programming, the analytical expression of the sensitivity of the Jacobian matrix element is derived, and then the stability sensitivity is obtained using the chain rule of differentiation. Specifically: First, the original form of the above semidefinite programming problem is changed to the standard form: ;

[0034] where , the vector includes the stability index and the lower triangular elements of the symmetric matrix , , . Considering all the constraints in the original semidefinite programming, define where , , represents the set of all n-dimensional real symmetric matrices. Corresponding to the constraints in the aforementioned original semidefinite programming, , , , , , , , , , represents the basis of the n-dimensional symmetric matrix, .

[0035] Next, write out the standard form of the dual problem of the above semidefinite programming problem: ;

[0036] Among them, the symmetric matrix Z represents the dual variable of the original variable .

[0037] Then, according to the Slater condition, there exists a strictly feasible solution of the primal problem , such that . At the same time, there exists a strictly feasible solution of the dual problem, satisfying and , . This condition guarantees the strong duality of the semidefinite programming problem, and the duality gap at the optimal value is 0: . Also, because and , it can be obtained that: ;

[0038] Since the proposed semidefinite programming problem is based on matrix inequalities, while the standard convex problem is based on scalar inequalities, in order to conveniently derive the parameter sensitivity using the dual variables, the "svec" calculation is introduced to vectorize the matrices in the semidefinite programming problem, obtaining the standard convex optimization form, and then establishing the parameter sensitivity formula of the semidefinite programming problem in the way of traditional convex problems.

[0039] To facilitate representation and matrix operations, define the function "svec": map to , . Then, through the "svec" function and the inner product, establish the relationship between matrix and vector calculations: ; ; , then the above formula is expressed as: ; Since the duality gap is 0, it can be obtained that: ;

[0040] Use the symmetric Kronecker product to simplify the expression. Its definition is that for any n-dimensional symmetric matrix X, there exist M, N ∈ , such that: ; Therefore is expressed as: ;

[0041] Then, by combining and , the function G is defined as: ;

[0042] wherein, , at the optimal value of the given parameter . Substantially, G is regarded as a variant of the KKT condition under the matrix inequality. Since both c and are continuously differentiable, the derivative of the function is expressed as: ;

[0043] is non-singular at the optimal value , and the calculation formula for the parameter sensitivity is: ; wherein, the derivative is expressed as: ; It should be noted that the first element of the vector is the stability index . For the sake of concise expression, the vector containingis defined. Therefore, the stability index is also the first element of .

[0044] Finally, by applying the chain rule of differentiation, the sensitivity of the stability index to the controllable variable, i.e., the ratio of the network-forming converters, is obtained: ; wherein, d is the partial derivative of the Jacobian matrix element containing with respect to . Since each Jacobian matrix element is an explicit function related to

[0045] , this partial derivative can be conveniently derived. S3. Initialize the ratio of the network-forming converters, and iterate with the stability sensitivity of the ratio of the network-forming converters as the gradient until the objective function value reaches the stability index limit value or the difference between the objective function values of two consecutive iterations is less than the convergence gap and then stop, so as to obtain the optimal ratio of the network-forming converters.

[0046] Initialize the ratio of the network-forming converters as the upper limit of the network-forming converter ratio of the substation, set the stability index limit value as , and the optimization algorithm process is asFigure 4 As shown in the figure, specifically: S31. Set the initial value of the configuration network type converter ratio parameter participating in the optimization , let .

[0047] S32. Calculate the objective function value according to the method in step S2 and the stability sensitivity .

[0048] S33. Judge the termination condition, specifically: Termination condition 1: When , the difference between the objective function values of two iterations satisfies the convergence gap ε, that is: ; Termination condition 2: When the stability index is within the limit range , that is: ; If any termination condition is met, the algorithm stops and outputs the optimization result. If none of the termination conditions are met, go to step S34 to iteratively update the configuration network type converter ratio parameter.

[0049] S34. Iteratively update the configuration network type converter ratio d : ; Among them, is the iteration step size. Substitute the updated into step S32, and let .

[0050] The method of the present invention will be described below through a specific example. Table 1 shows the main parameters of the new energy power station, configuration network type and grid-following type converters in the example of the present invention. Taking the weak grid condition with a short-circuit ratio of 1.2 during the operation of the power station as an example, the optimization of the configuration network type ratio is carried out.

[0051] Table 1 Main parameters of new energy power station, configuration network type and grid-following type converters ; To verify the accuracy and rapidity of the sensitivity analysis formula in step S2, the above scenario is applied to calculate and test the stability sensitivity.

[0052] The test is carried out on a computing platform equipped with an Intel i5-12450H CPU processor and 16GB of memory. 100 configuration network type converter ratios are randomly generated to calculate the sensitivity and record the cumulative calculation time. To illustrate the significant improvement in calculation accuracy and efficiency, three disturbance values , , , the sensitivity is calculated using the numerical perturbation method for comparison.

[0053] The analytical method of this paper, the numerical perturbation method, the numerical perturbation method, the numerical perturbation method are respectively used to calculate the stability sensitivity under these 100 grid-forming converter ratios, and a relative error graph of the calculation results compared with the analytical reference value under these 100 scenarios is obtained, as Figure 5 shown. The maximum and average relative errors in 100 scenarios are statistically analyzed, and the cumulative calculation time is recorded, as shown in Table 2. By comparison, it can be seen that the sensitivity analytical formula in step S2 can accurately analyze the stability sensitivity. At the same time, compared with the numerical perturbation method, the cumulative calculation time is shortened to less than half, showing a significant improvement in the calculation speed.

[0054] Table 2 Calculation accuracy and efficiency of the numerical perturbation method and the method proposed in the present invention ; To verify the effectiveness of the optimization algorithm in step S3, the stability index limit value is set to , and the range is . The optimal grid-forming converter ratio in the aforementioned scenario is obtained as 9.0%. A perturbation of 0.05 p.u. is added to the active power command at 5 s under each ratio, and the comparison of the output active power curves is as Figure 6 shown. It can be seen from the figure that when the grid-forming converter ratio is 9.0%, the stability index is -0.559, which meets the constraint of the stability index limit value. When the grid-forming converter ratios are 8.5% and 8.0%, the stability indices are -0.230 and 0.102 respectively, which do not meet the constraint of the stability index limit value. Therefore, the optimization algorithm in step S3 can effectively obtain the optimal grid-forming converter ratio that meets the constraint of the stability index limit value.

[0055] Therefore, the present invention adopts the above-mentioned method for the capacity ratio of grid-forming and grid-following converters based on semidefinite programming, which can use the duality of semidefinite programming to analytically obtain the stability sensitivity and realize the accurate and rapid solution of the optimal grid-forming converter ratio.

[0056] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify or equivalently replace the technical solutions of the present invention, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for capacity matching of grid-forming and grid-following converters based on semi-definite programming, characterized in that: The following steps are involved: S1. Establish state space models of grid-forming converters and grid-following converters respectively, and construct the overall state space model of the station including grid-forming converters and grid-following converters through coordinate transformation; S2. Use the semidefinite programming based on Lyapunov equation to describe the stability index, and derive the stability sensitivity analytical expression of the grid-type converter ratio according to the original variable and dual variable of the semidefinite programming; S3. Initialize the grid-type converter ratio, and iterate with the stability sensitivity of the grid-type converter ratio as the gradient until the objective function value reaches the stability index limit or the difference between the objective function values ​​of two iterations is less than the convergence gap, and then stop, to obtain the optimal grid-type converter ratio.

2. According to claim 1, a method for matching capacity of grid-forming and grid-following converters based on semidefinite programming, characterized in that: In S1, the wind and solar stations include Grid-type converter and The grid-type converter uses equivalent impedance Z c Connected to the power grid; The construction process of the overall state space model of the station is as follows: The mathematical model of each control link and filter circuit of the grid-following converter is: ； In the formula, , They are the phase angle and frequency obtained by the grid-type phase-locked loop, , They are the phase-locked loop PI parameters, , They are the power outer loop PI parameters, , They are the current inner loop PI parameters, , are the active and reactive power output of the converter respectively, represents the reference value, is the filter inductor, , are the filter outlet current and voltage respectively, represents the reference value, is the converter output voltage.

3. The method for capacity matching of grid-forming and grid-following converters based on semidefinite programming according to claim 2 is characterized in that: The mathematical models of each control link and filter circuit of the grid-type converter are as follows: ； In the formula, The frequency obtained for network-based virtual synchronous control is D , J are the damping coefficient and inertia of the virtual synchronous control loop, E is the internal potential obtained by voltage droop control, is the voltage droop coefficient, k pv , k iv They are the voltage outer loop PI parameters, k pc , k ic They are the current inner loop PI parameters, P , are the active and reactive power output of the converter respectively, represents the reference value, L f is the filter inductor, , are the filter outlet current and voltage respectively, represents the reference value, is the converter output voltage.

4. The method for capacity matching of grid-forming and grid-following converters based on semidefinite programming according to claim 3 is characterized in that: The mathematical models of the grid-following converter, grid-forming converter and AC network are combined through coordinate transformation and linearized at the equilibrium point to obtain the overall state space model of the station: ； In the formula, is the system state variable, the matrix A is the system state matrix, the small signal stability of the system is related to the matrix A is related to the eigenvalues ​​of .

5. The method for capacity matching of grid-forming and grid-following converters based on semidefinite programming according to claim 1 is characterized in that: In S2, the Lyapunov equation is used to describe the stability of the system. Lyapunov's second method states that if and only if there exists a real symmetric positive definite matrix satisfy , the system is asymptotically stable, and the related Lyapunov function is , is any given negative real number; The stability index is further designed as the solution to the following semidefinite programming problem: ； The Lyapunov equation requires , so set a constant that tends to 0 Make , which is consistent with is equivalent to setting , if the system is stable, the stability index obtained by semidefinite programming is will be negative; Stability index The absolute value of is the lower limit of the convergence speed after perturbation, and from the above semidefinite programming problem: ； Define an analytical formula for accurately calculating stability sensitivity, and derive the sensitivity of Jacobian matrix elements from the convexity of semidefinite programming The analytical expression of the stability sensitivity is obtained by using the chain rule. .

6. A method for capacity matching of grid-forming and grid-following converters based on semidefinite programming according to claim 5, characterized in that: Stability Sensitivity The specific derivation method is: First, change the original form of the semidefinite programming problem above into the standard form: ； in, ,vector Including stability indicators and the symmetric matrix The lower triangular elements of , , ; Consider all constraints in the original semidefinite program and define ,in , , Indicates all A set of dimensional real symmetric matrices; corresponding to the constraints in the aforementioned original semidefinite programming, , , , , , , , , , represent The basis of the symmetric matrix, ; Next, write the standard form of the dual problem of the above standard form of semidefinite programming problem: ； Among them, the symmetric matrix Z Represents the original variable The dual variable of Then, according to the Slater condition, there exists a strictly feasible solution to the original problem , so that , and there exists a strictly feasible solution to the dual problem that satisfies and , ; This condition ensures the strong duality of the semidefinite programming problem, at the optimal value The duality gap at is 0: ; and because and ,have to: ； Since the proposed semidefinite programming problem is based on matrix inequality, and the standard convex problem is based on scalar inequality, in order to conveniently derive parameter sensitivity using dual variables, the "svec" calculation is used to vectorize the matrix in the semidefinite programming problem to obtain the standard convex optimization form, and then the parameter sensitivity formula of the semidefinite programming problem is established in the way of traditional convex problem; In order to facilitate the representation and matrix operations, define the function "svec": Mapping , ; Then, the relationship between matrix and vector calculation is established through the "svec" function and inner product: ； ； make , then the above formula is expressed as: ； Since the duality gap is 0, we have: ； Using symmetric Kronecker products To simplify the expression, it is defined as dimensional symmetric matrix X ,exist M , N ∈ , so that: ； therefore It is expressed as: ； Then, by combining and , define the function G : ； in, , given the parameters The optimal value of Department ;Will G can be regarded as a variant of the KKT condition under matrix inequality, since c and are all continuously differentiable, and the derivative of the function is expressed as: ； At the optimal value is non-singular, parameter sensitivity The calculation formula is: ； Among them, the derivative It is expressed as: ； vector The first element is the stability index , for the sake of simplicity, we define Vector , so the stability index Too The first element of Finally, by applying the chain rule, we obtain the stability index Sensitivity to the controllable variable, i.e. the grid-connected converter ratio: ； in, is the Jacobian matrix element pair containing d The partial derivative of .

7. The method for capacity matching of grid-forming and grid-following converters based on semidefinite programming according to claim 6 is characterized in that: In S3, the initialization grid-type converter ratio is the upper limit of the station grid-type converter ratio. , setting the stability index limit to , the optimization algorithm process is as follows: S31. Setting the initial value of the ratio parameter of the grid-connected converter involved in the optimization ,make ; S32, according to the method in step S2, calculate the objective function value Sensitivity and stability ; S33, determining the termination condition; S34, iterative update of grid-connected converter ratio : ； in, is the iteration step, and the updated Substitute into step S32, let .

8. The method for capacity matching of grid-forming and grid-following converters based on semidefinite programming according to claim 7 is characterized in that: In S33, specifically: Termination condition 1: When When , the difference between the objective function values ​​of the two iterations satisfies the convergence gap ε, that is: ； Termination condition 2: When the stability index is within the limit Range Within, that is: ； If any of the termination conditions is met, the algorithm stops and outputs the optimization result. If none of the termination conditions is met, the algorithm goes to step S34 to iteratively update the grid-connected converter matching parameters.

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