Method for suppressing three-phase global capacitor voltage ripple of mmc based on semi-definite relaxation

Abstract

The application discloses a kind of MMC three-phase global capacitor voltage ripple suppression methods based on semi-definite relaxation, eliminate trigonometric function nonlinearity by orthogonal rectangular coordinate transformation, and construct three-phase global cost function containing 1 / ( iω ) 2 Weight, optimize three-phase energy fluctuation simultaneously, avoid other phase voltage divergence caused by single-phase local optimum.Simultaneously, the application is by semi-definite relaxation cooperation trace heuristic low rank penalty, non-convex quadratic constraint quadratic programming is lossless convex into strict semi-definite programming, obtain three-phase capacitor voltage ripple global optimal solution, overcome the defects of insufficient precision of iterative enumeration or neural network approximation method;Further, the extraction global optimal second harmonic circulating current and third harmonic voltage reference are combined positive and negative sequence voltage reference to generate modulation wave and trigger pulse.The application can realize the global optimal collaborative suppression of three-phase capacitor voltage ripple, avoid voltage divergence caused by single-phase method.

Description

Technical Field

[0001] This invention belongs to the field of new energy power distribution and transmission control technology, specifically relating to a method for suppressing three-phase global capacitor voltage ripple based on semi-deterministic relaxation (MMC). Background Technology

[0002] Modular multilevel converters (MMCs) are a core technology for high-voltage direct current (HVDC) transmission. Under unbalanced grid conditions, the active power load of each phase of the MMC varies significantly. External asymmetrical power disrupts the internal energy balance, causing drastic fluctuations in the energy of the excitation arms. This leads to the submodule capacitor voltage deviating from the safe operating range, and in severe cases, system shutdown. Therefore, suppressing capacitor voltage ripple is crucial to ensuring the safe and stable operation of the MMC.

[0003] Existing capacitor voltage ripple suppression strategies are mostly based on circulating current or common-mode voltage injection, such as in the literature [Xu J, Deng W, Li G. Optimal second harmonic current injection for suppressing voltage fluctuations in hybrid MMC capacitors under single-phase ground faults on the grid side. IEEE Transactions on Power Transmission, 2022, Vol. 37, No. 4: pp. 2857-2866]. However, most of these strategies assume a three-phase balanced operating condition. But under unbalanced operating conditions, the injected second harmonic circulating current and third harmonic voltage cannot be completely decoupled between the three phases, and the local optimal solution for a single phase can easily lead to voltage divergence in other phases. Furthermore, the accurate global voltage balance model itself is a non-convex quadratic constrained quadratic programming problem involving trigonometric function nonlinearity. Existing methods typically employ approximations such as iterative enumeration [Xu J, Wang J, Yang Y. Optimal suppression strategy for hybrid MMC capacitor voltage ripple under grid voltage imbalance. IEEE Transactions on Electric Power Transmission, 2023, Vol. 38, No. 1: pp. 244-254] or neural networks [Wang S, Dragicevic T, Teodorescu R. Learning-based suppression of capacitor voltage ripple in modular multilevel converters under different power factor imbalance grid conditions. Proceedings of the 11th IEEE International Symposium on Power Electronics for Distributed Generation Systems, 2020: pp. 531-535], sacrificing model accuracy and failing to obtain the true global optimal solution.

[0004] Therefore, there is an urgent need for a method that can achieve globally optimal suppression of three-phase capacitor voltage ripple under unbalanced operating conditions. Summary of the Invention

[0005] To address the problem that existing MMC capacitor voltage ripple suppression methods under unbalanced operating conditions, which rely on single-phase local optimization or approximate solutions, often fail to obtain a globally optimal solution for all three phases and are prone to causing partial phase capacitor voltage ripple divergence, this invention provides a three-phase global capacitor voltage ripple suppression method based on semi-definite relaxation. This method can achieve globally optimal collaborative suppression of three-phase capacitor voltage ripple and avoid voltage divergence caused by single-phase methods.

[0006] A method for suppressing three-phase global capacitor voltage ripple in MMC based on semi-deterministic relaxation includes the following steps: Step S1: Obtain the DC voltage, three-phase AC current, and positive and negative sequence voltage command values ​​given by the outer loop of the MMC, and calculate the DC bias current of each phase of the MMC based on the principle of instantaneous power balance of each phase. Step S2: Construct an augmented vector based on the second harmonic circulating current and the third harmonic voltage to be injected. x The amplitude coefficients of the power fundamental frequency to third harmonic of each phase arm of the MMC are reconstructed as follows: x The quadratic function is used to construct a non-convex QCQP (quadratic constraint quadratic programming) model based on the global cost function; Step S3: Use semidefinite relaxation to convexify the non-convex QCQP model to obtain the globally optimal semidefinite relaxation matrix, and extract the second harmonic circulating current reference value and the third harmonic voltage reference value from it. Step S4: Combine the second harmonic circulating current reference value and the third harmonic voltage reference value with the positive and negative sequence voltage command values ​​to generate bridge arm modulation waves and trigger pulses for MMC control.

[0007] Further, in step S1, the DC bias current of each phase of the MMC is calculated using the following expression: in: I dcj For MMC j Phase DC bias current, I acj For MMC j Phase alternating current, U dc This is the DC voltage of the MMC. U ac,j+ and i j+ They are respectively j The magnitude and phase angle of the positive sequence voltage. U ac,j- and i j- They are respectively j The magnitude and phase angle of the negative sequence voltage. for j Phase angle of the current in the phase,j =a,b,c.

[0008] Furthermore, the augmented vector in step S2 x =[1, I 2x , I 2y , U 3x , U 3y ] T ,in I 2x and I 2y These are the rectangular coordinate components of the second harmonic circulation. U 3x and U 3y The rectangular coordinate components of the third harmonic voltage are represented by the superscript. T The term indicates transpose; the second harmonic circulating current is a symmetrical negative sequence component with equal amplitudes in all three phases and a phase difference of 2π / 3; the third harmonic voltage is a zero-sequence common-mode component with the same amplitude and phase in all three phases.

[0009] Furthermore, the expression for the non-convex QCQP model in step S2 is as follows: in: F flu ( x (Regarding) x The global cost function, i For harmonic order and i =1,2,3 oh M is the angular frequency of the power grid. I and M U It is a constant diagonal matrix. I in,max The maximum permissible amplitude of the injected second harmonic circulating current. U in,max The maximum permissible magnitude of the injected third harmonic voltage. Q Aij and Q Bij It is a 5×5 real symmetric matrix.

[0010] Furthermore, the real symmetric matrix Q Aij and Q Bij The expression is as follows: in: c Aij andc Bij They represent j Mutually i Sine and cosine scalars of subharmonics H Aij and H Bij They represent j Mutually i Sine and cosine core coupling submatrix of subharmonics v Aij and v Bij They represent j Mutually i The sine and cosine column vectors of the subharmonics.

[0011] Furthermore, the sinusoidal scalar c Aij Sum of cosine scalars c Bij The expression is as follows: in: I dcj For MMC j Phase DC bias current, I acj For MMC j Phase alternating current, U dc This is the DC voltage of the MMC. L arm For the bridge arm inductor of MMC, U ac,j+ and i j+ They are respectively j The magnitude and phase angle of the positive sequence voltage. U ac,j- and i j- They are respectively j The magnitude and phase angle of the negative sequence voltage. for j The phase angle of the current in the phase.

[0012] Furthermore, the sinusoidal core coupling sub-matrix H Aij Cosine core coupling submatrix H Bij The expression is as follows: in: d 2j For the second harmonic negative sequence circulation in j The phase angle of the phase and d 2a =0, d 2b =2π / 3, d 2c =-2π / 3.

[0013] Furthermore, the sinusoidal column vector v Aij Sum and cosine column vectors v Bij The expression is as follows: Among them: A ij for j Mutually i The amplitude coefficient of the sinusoidal term of the subharmonic power and A ij = x T Q Aij x B ij for j Mutually i The amplitude coefficient of the cosine term of the subharmonic power and B ij = x T Q Bij x , I 2x and I 2y The rectangular coordinate components of the second harmonic circulation are shown. U 3x and U 3y The rectangular coordinate components of the third harmonic voltage are given.

[0014] Furthermore, the specific implementation of step S3 is as follows: First, define a semi-definite relaxation matrix. Z = xx T Reduce all quadratic forms to linear functions, i.e., A ij =Tr( Q Aij Z ), B ij =Tr( Q Bij ZThen, the non-convex QCQP model is transformed into a semi-positive definite programming problem, and the matrix is ​​forced through the trace penalty term. Z Converging toward the rank=1 boundary, we obtain the following objective function: Where: Tr() represents the trace of the matrix, Represents the constraint matrix Z The eigenvalues ​​in the matrix are all greater than or equal to 0. l E represents the weighting coefficient of the trace penalty term. 11 Let rank be a constant diagonal matrix, and let rank be a semidefinite relaxation matrix. Z rank; Finally, the interior point method is used to solve the above objective function to obtain the unique globally optimal semidefinite relaxation matrix that satisfies the rank=1 property. Then, the rectangular coordinate components of the second harmonic circulating current and the third harmonic voltage are extracted from it through eigenvalue decomposition and used as reference values.

[0015] A computer device includes a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the above-described method for suppressing MMC three-phase global capacitor voltage ripple based on semi-deterministic relaxation.

[0016] A computer-readable storage medium storing a computer program, which, when executed by a processor, implements the above-described method for suppressing MMC three-phase global capacitor voltage ripple based on semi-definite relaxation.

[0017] Based on the above technical solution, the present invention has the following beneficial technical effects: 1. This invention eliminates the nonlinearity of trigonometric functions through orthogonal rectangular coordinate transformation and constructs a system containing 1 / ( yes ) 2 The weighted three-phase global cost function simultaneously optimizes three-phase energy fluctuations, avoiding voltage divergence in other phases caused by local optima in a single phase.

[0018] 2. This invention transforms a non-convex quadratic constrained quadratic programming problem into a strictly positive semidefinite programming problem without loss through a semidefinite relaxation trace heuristic low-rank penalty, thereby obtaining the global optimal solution for the three-phase capacitor voltage ripple and overcoming the shortcomings of insufficient accuracy of iterative enumeration or neural network approximation methods. Attached Figure Description

[0019] Figure 1 This is a schematic flowchart of the MMC three-phase global capacitor voltage ripple suppression method of the present invention.

[0020] Figure 2 This is a schematic diagram of the submodule voltage waveforms of the three-phase upper and lower bridge arms of the MMC system in an embodiment of the present invention. Detailed Implementation

[0021] To describe the present invention in more detail, the technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0022] like Figure 1 As shown, this embodiment provides a method for suppressing MMC three-phase global capacitor voltage ripple based on semi-definite relaxation. The specific implementation process is as follows: Step S1: Reconstruct the DC bias current of each phase.

[0023] Obtain the positive and negative sequence voltage references and AC side current given by MMC, calculate the DC bias current of each phase based on the principle of instantaneous power balance of each phase, reflect the unbalanced active power load in the DC side current distribution, and solve the DC power mismatch of each phase arm caused by the traditional equal DC current sharing logic.

[0024] The three-phase current on the AC side of the MMC is expressed as follows: I acj The outer loop voltage positive and negative sequence command values ​​of the MMC voltage controller are represented as follows: U d+ , U q+ , U d- , U q- The DC-side voltage of MMC is expressed as U dc The transformation from a two-phase rotating coordinate system to a three-phase stationary coordinate system can... U d+ , U q+ , U d- , U q- Convert to three-phase voltage U a , U b , U c Taking phase a as an example, its positive and negative sequence voltages can be calculated using the following formula: in: U ac,a+ , U ac,a- , U ac,a0 These are the positive-sequence voltage, negative-sequence voltage, and zero-sequence voltage of phase a on the MMC AC side. α For e j2 π / 3 .

[0025] Therefore, the DC bias current of each phase Idcj It can be calculated using the following formula: in: I dcj For MMC j Phase DC bias current, I acj For MMC j Phase alternating current, U dc This is the DC voltage of the MMC. U ac,j+ and i j+ They are respectively j The magnitude and phase angle of the positive sequence voltage. U ac,j- and i j- They are respectively j The magnitude and phase angle of the negative sequence voltage. for j The phase angle of the current in the phase is j Phase current relative to j The phase difference of the phase voltage is extracted separately through a phase-locked loop. j The phase angle is obtained by subtracting the phase angle of the phase voltage and the phase angle of the current. j =a,b,c.

[0026] Step S2: Cartesian coordinate system transformation, power harmonic quadratic reconstruction, and construction of a weighted global cost function QCQP model.

[0027] Firstly, by j The voltage and current in the upper arm of the phase are decomposed into fixed components and injected components, and can be reconstructed as follows: in: i pj and u pj These are the total current and total voltage of the upper bridge arm, respectively. i nor and i inj These are the fixed current component and the injected current component, respectively. u nor and u inj These are the fixed voltage component and the injected voltage component, respectively.

[0028] The fixed components of current and voltage can be calculated using the following formula: in: oh The angular frequency of the power grid. L arm For bridge arm inductance.

[0029] Define a three-phase shared four-dimensional global decision vector Y =[ I 2x , I 2y , U 3x , U 3y ] T And construct augmented vectors x =[1, I 2x , I 2y , U 3x , U 3y ] T ,in I 2x and I 2y To inject the rectangular coordinate components of the second harmonic circulation, U 3x and U 3y Assuming the rectangular coordinate components of the injected third harmonic voltage, the injected current and voltage components can be expressed as: in: d 2j It is a second-harmonic negative-sequence circulation in j The phase angle of the phase has d 2a =0, d 2b =2π / 3, d 2c =-2π / 3; The injected second harmonic circulating current is a symmetrical negative sequence component with equal amplitude and phase difference of 2π / 3 in all three phases. The injected third harmonic voltage is a zero sequence common mode component with equal amplitude and phase in all three phases.

[0030] No. j Phase upper arm instantaneous power P pj = u pj i pj Expanded by the following formula, it is the sum of the DC component and the sinusoidal / cosine components from the fundamental frequency to the third harmonic: in: P 0 represents the average power of the upper bridge arm, A1, A2, and A3 are the amplitude coefficients of the power sine term, and B1, B2, and B3 are the amplitude coefficients of the power cosine term.

[0031] Upper arm voltage u pj Calculated from DC voltage, phase AC voltage, and injected third harmonic voltage: in: U mj for j Phase AC voltage amplitude, i j The voltage phase angle, U 3 represents the amplitude of the injected third harmonic voltage. The phase angle of the injected third harmonic voltage.

[0032] The upper arm current can be determined by the DC bias current. I dcj With alternating current calculation: in: I mj for j Phase alternating current amplitude, I 2 and These represent the amplitude and phase of the injected second harmonic current, respectively. The power factor angle.

[0033] The bridge arm power amplitude coefficient is reconstructed to A ij = x T Q Aij x B ij = x T Q Bij x , where the matrix Q Aij and Q Bij It is a 5×5 real symmetric matrix: scalar c Aij and c Bij and 4-dimensional column vectors v Aij and v BijThe 4×4 core coupling submatrix is ​​determined by the external steady-state power of the MMC and the independent linear power terms of each phase. H Aij and H Bij Source I 2 and U 3. Quadratic bilinear coupling: When harmonic number i =2 or i When =3, H A2j , H B2j , H A3j , H B3j A matrix that is always zero.

[0034] scalar c Aij and c Bij It can be calculated from the invariant term in the product of current and voltage. c Aij and c Bij for u nor and i nor The first frequency term of the product: 4-dimensional column vector v Aij and v Bij Here are the partial derivatives of the coefficients with respect to the injected variables at the zero-injection operating point: in: i =1,2,3 j =a,b,c.

[0035] The global optimization function can then be expressed as: in: I in,max The maximum permissible amplitude of the injected second harmonic circulating current. U in,max M represents the maximum permissible magnitude of the injected third harmonic voltage. I and MU It is a constant diagonal matrix, represented as: Step S3: Semidefinite relaxation convexity transformation, trace penalty, interior point method solution, eigenvalue decomposition to extract the optimal reference.

[0036] Define a semidefinite relaxation matrix Z = xx T Reduce all quadratic forms to linear functions, i.e., A ij =Tr( Q Aij Z ), B ij =Tr( Q Bij Z ).

[0037] in: .

[0038] At the same time, a trace penalty term is introduced. l Tr( Z ), through the penalty matrix Z The trace forces it to converge to the rank-one boundary, ensuring the compactness of the semidefinite relaxation. The objective function and constraints can be further expressed as: in: Weighting coefficient l The value of should match the magnitude of each term in the objective function. l Too small a value cannot effectively punish rank augmentation, leading to Z The rank-1 constraint is not satisfied. l An excessively large penalty term will cause the objective function to dominate, leading to an optimization result that deviates from the optimal solution of the original QCQP. Specifically, an iterative method can be used to determine this: l =10 -3 Using the initial values ​​to solve a semidefinite programming problem, if the resulting matrix... Z If the rank is greater than 1, then... l Increase the value by a factor of 2 and solve again until the rank-1 condition is met. l The typical range of values ​​is

[10] . -3 10 -2 In this embodiment, it is determined that... l =0.016.

[0039] Therefore, the problem is transformed into a semidefinite programming problem, which can be solved using the interior-point method to obtain the unique globally optimal matrix that satisfies the rank=1 property. From eigenvalue decomposition Extracting the principal feature vector to recover , , , Among them, for The expression for eigenvalue decomposition is as follows: in: V It is an orthogonal matrix. It is a diagonal matrix composed of eigenvalues. s k For the first k 1 eigenvalue, s 1≥ s 2≥ s 3≥ s 4≥ s 5≥0 is eigenvalues, v k For the first k The eigenvectors corresponding to each eigenvalue; due to ,have s 1 > 0 and s 2= s 3= s 4= s 5≈0.

[0040] Take the largest eigenvalue s eigenvector corresponding to 1 v 1 (i.e., orthogonal matrix) V The first column of the vector is the estimated value of the augmented vector. : Since the first element of the augmented vector is always 1, it is necessary to... v 1. After normalization, we can obtain : in:[ v 1] i for v 1 of i Each component.

[0041] Step S4: Combine voltage reference to generate bridge arm modulation wave and trigger pulse.

[0042] Reference command for positive and negative sequence voltages U d+ , U q+ , U d- , U q- With second harmonic circulating current and third harmonic voltage reference , , , Combined, a bridge arm modulation wave and a trigger pulse are generated.

[0043] This embodiment takes a system with a ±500kV MMC-HVDC (high voltage direct current transmission) connecting 300 1.5MW permanent magnet synchronous wind turbine units as an example. The rated AC voltage of the system is 150kV, the number of sub-modules per MMC arm is 250, the capacitor is 15mF, and the rated voltage is 2kV.

[0044] Figure 2 The diagram illustrates the voltage waveforms of the three-phase upper and lower bridge arm submodules of an MMC system before and after applying the method of this invention. Before the black dashed line, the traditional method was used, resulting in a capacitor voltage ripple of 0.22kV for phase a, 0.26kV for phase b, and 0.24kV for phase c. After the black dashed line, the method of this invention was applied, reducing the capacitor voltage ripple of phase a to 0.14kV, phase b to 0.20kV, and phase c to 0.18kV. The voltage ripple of the submodules in all three phases was effectively reduced, demonstrating that the method of this invention can effectively reduce MMC capacitor voltage ripple and verifying the effectiveness of the invention.

[0045] The above description of the embodiments is provided to enable those skilled in the art to understand and apply the present invention. Those skilled in the art can readily make various modifications to the above embodiments and apply the general principles described herein to other embodiments without creative effort. Therefore, the present invention is not limited to the above embodiments, and any improvements and modifications made to the present invention by those skilled in the art based on the disclosure thereof should be within the scope of protection of the present invention.

Claims

1. A method for suppressing three-phase global capacitor voltage ripple based on semi-definite relaxation MMC, characterized in that, Includes the following steps: Step S1: Obtain the DC voltage, three-phase AC current, and positive and negative sequence voltage command values ​​given by the outer loop of the MMC, and calculate the DC bias current of each phase of the MMC based on the principle of instantaneous power balance of each phase. Step S2: Construct an augmented vector based on the second harmonic circulating current and the third harmonic voltage to be injected. x The amplitude coefficients of the power fundamental frequency to third harmonic of each phase arm of the MMC are reconstructed as follows: x The quadratic function is used to construct a nonconvex QCQP model based on the global cost function; Step S3: Use semidefinite relaxation to convexify the non-convex QCQP model to obtain the globally optimal semidefinite relaxation matrix, and extract the second harmonic circulating current reference value and the third harmonic voltage reference value from it. Step S4: Combine the second harmonic circulating current reference value and the third harmonic voltage reference value with the positive and negative sequence voltage command values ​​to generate bridge arm modulation waves and trigger pulses for MMC control.

2. The method for suppressing MMC three-phase global capacitor voltage ripple based on semi-deterministic relaxation according to claim 1, characterized in that, In step S1, the DC bias current of each phase of the MMC is calculated using the following expression: in: I dcj For MMC j Phase DC bias current, I acj For MMC j Phase alternating current, U dc This is the DC voltage of the MMC. U ac,j+ and θ j+ They are respectively j The magnitude and phase angle of the positive sequence voltage. U ac,j- and θ j- They are respectively j The magnitude and phase angle of the negative sequence voltage. for j Phase angle of the current in the phase, j =a,b,c.

3. The method for suppressing MMC three-phase global capacitor voltage ripple based on semi-deterministic relaxation according to claim 1, characterized in that: The augmented vector in step S2 x =[1, I 2x , I 2y , U 3x , U 3y ] T ,in I 2x and I 2y These are the rectangular coordinate components of the second harmonic circulation. U 3x and U 3y The rectangular coordinate components of the third harmonic voltage are represented by the superscript. T The term indicates transpose; the second harmonic circulating current is a symmetrical negative sequence component with equal amplitudes in all three phases and a phase difference of 2π / 3; the third harmonic voltage is a zero-sequence common-mode component with the same amplitude and phase in all three phases.

4. The method for suppressing MMC three-phase global capacitor voltage ripple based on semi-deterministic relaxation according to claim 1, characterized in that, The expression for the non-convex QCQP model in step S2 is as follows: in: F flu ( x (Regarding) x The global cost function, i For harmonic order and i =1,2,3 ω M is the angular frequency of the power grid. I and M U It is a constant diagonal matrix. I in,max The maximum permissible amplitude of the injected second harmonic circulating current. U in,max The maximum permissible magnitude of the injected third harmonic voltage. Q Aij and Q Bij It is a 5×5 real symmetric matrix.

5. The method for suppressing MMC three-phase global capacitor voltage ripple based on semi-deterministic relaxation according to claim 4, characterized in that, The real symmetric matrix Q Aij and Q Bij The expression is as follows: in: c Aij and c Bij They represent j Mutually i Sine and cosine scalars of subharmonics H Aij and H Bij They represent j Mutually i Sine and cosine core coupling submatrix of subharmonics v Aij and v Bij They represent j Mutually i The sine and cosine column vectors of the subharmonics.

6. The method for suppressing MMC three-phase global capacitor voltage ripple based on semi-deterministic relaxation according to claim 5, characterized in that, The sine scalar c Aij Sum of cosine scalars c Bij The expression is as follows: in: I dcj For MMC j Phase DC bias current, I acj For MMC j Phase alternating current, U dc This is the DC voltage of the MMC. L arm For the bridge arm inductor of MMC, U ac,j+ and θ j+ They are respectively j The magnitude and phase angle of the positive sequence voltage. U ac,j- and θ j- They are respectively j The magnitude and phase angle of the negative sequence voltage. for j The phase angle of the current in the phase.

7. The method for suppressing MMC three-phase global capacitor voltage ripple based on semi-deterministic relaxation according to claim 5, characterized in that, The sinusoidal core coupling submatrix H Aij Cosine core coupling submatrix H Bij The expression is as follows: in: δ 2j For the second harmonic negative sequence circulation in j The phase angle of the phase and δ 2a =0, δ 2b =2π / 3, δ 2c =-2π / 3.

8. The method for suppressing MMC three-phase global capacitor voltage ripple based on semi-deterministic relaxation according to claim 5, characterized in that, The sinusoidal column vector v Aij Sum and cosine column vectors v Bij The expression is as follows: Among them: A ij for j Mutually i The amplitude coefficient of the sinusoidal term of the subharmonic power and A ij = x T Q Aij x B ij for j Mutually i The amplitude coefficient of the cosine term of the subharmonic power and B ij = x T Q Bij x , I 2x and I 2y These are the rectangular coordinate components of the second harmonic circulation. U 3x and U 3y The rectangular coordinate components of the third harmonic voltage are given.

9. The method for suppressing MMC three-phase global capacitor voltage ripple based on semi-deterministic relaxation according to claim 8, characterized in that, The specific implementation of step S3 is as follows: First, define a semidefinite relaxation matrix. Z = xx T Reduce all quadratic forms to linear functions, i.e., A ij =Tr( Q Aij Z ), B ij =Tr( Q Bij Z Then, the non-convex QCQP model is transformed into a semi-positive definite programming problem, and the matrix is ​​forced through the trace penalty term. Z Converging toward the rank=1 boundary, we obtain the following objective function: Where: Tr() represents the trace of the matrix, Represents the constraint matrix Z The eigenvalues ​​in the matrix are all greater than or equal to 0. λ E represents the weighting coefficient of the trace penalty term. 11 Let rank be a constant diagonal matrix, and let rank be a semidefinite relaxation matrix. Z rank; Finally, the interior point method is used to solve the above objective function to obtain the unique globally optimal semidefinite relaxation matrix that satisfies the rank=1 property. Then, the rectangular coordinate components of the second harmonic circulating current and the third harmonic voltage are extracted from it through eigenvalue decomposition and used as reference values.

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