MMC direct current port impedance modeling method adopting embedded repetitive controller

Abstract

An MMC direct current port impedance modeling method adopting an embedded repetitive controller relates to the technical field of harmonic suppression and impedance modeling of a flexible direct current power transmission system, and comprises the following steps: 1) constructing an MMC main circuit equivalent circuit; 2) converting the MMC equivalent circuit to a frequency domain; 3) calculating steady-state harmonic waves; 4) constructing a main circuit frequency domain linearization model; 5) constructing a control circuit frequency domain model; and 6) determining an MMC direct current port impedance model adopting the embedded repetitive controller. Based on multi-harmonic linearization, a complete double-closed-loop control structure is considered, accurate modeling is performed on the MMC system adopting the embedded repetitive controller, the accuracy of stability analysis is ensured, operation is convenient, and expansibility is high.

Description

Technical Field

[0001] The invention relates to the technical field of harmonic control and impedance modeling of a flexible direct current transmission system, and in particular to an MMC direct current port impedance modeling method using an embedded repetitive controller. Background Art

[0002] Modular multilevel converter (MMC) has been widely used in offshore wind power, variable speed drive and high voltage direct current transmission due to its high-quality output waveform, low switching device loss and powerful fault handling capability. With the large-scale grid connection of new energy generators, the power system has shown weak grid characteristics, and grid voltage asymmetry or voltage distortion has become more frequent. The MMC system has the risk of instability and the broadband oscillation problem is more serious. The embedded repetitive control technology based on the inner membrane principle has good harmonic suppression capability and is gradually being applied to the MMC system, which can improve the system operation performance and solve the harmonic pollution problem.

[0003] Impedance analysis is a common method for studying stability problems and analyzing the instability mechanism of the system. Establishing an accurate impedance model is the key to ensuring the effectiveness of the impedance analysis method. The multi-harmonic linearization method constructs the dynamic relationship between the harmonics of the system variables in the form of a matrix, which is conducive to expansion and calculation. It is one of the current mainstream impedance modeling methods. Due to the internal complexity of the MMC system, repetitive control will change the MMC impedance characteristics under the traditional control structure. Therefore, it is of great significance to carry out impedance analysis on the MMC system with an embedded repetitive control structure.

[0004] At present, there are still few studies on the DC side impedance modeling of MMC at home and abroad, and repetitive control will affect the DC side stability of the system. It is urgent to propose an MMC DC port impedance modeling method using an embedded repetitive controller to ensure the safe and reliable operation of the MMC system. Summary of the invention

[0005] In view of this, the present invention provides an MMC DC port impedance modeling method using an embedded repetitive controller, which solves the defects of the prior art.

[0006] The present invention provides a method for modeling the DC port impedance of an MMC using an embedded repetitive controller, characterized in that the method specifically comprises the following steps:

[0007] S1: Construct the equivalent circuit of the main circuit according to the mathematical model of MMC;

[0008] S2: Based on the modeling principle of multi-harmonic linearization, the MMC equivalent circuit is converted into the frequency domain and represented in the form of matrix and vector;

[0009] S3: simplifying the MMC frequency domain steady-state model, and calculating steady-state harmonics based on the model;

[0010] S4: Inject voltage disturbance into the DC port of the MMC to build a frequency domain linearization model of the main circuit under the action of the disturbance voltage;

[0011] S5: Based on the complete dual closed-loop control structure, a frequency domain model of the MMC control circuit is constructed;

[0012] S6: The frequency domain models of the main circuit and the control circuit are combined, and the calculation results of the steady-state harmonics are substituted into the frequency domain models, thereby obtaining the DC port impedance model of the MMC using the embedded repetitive controller;

[0013] Step 1) constructing a main circuit equivalent circuit of a modular multilevel converter according to an MMC dynamic equation;

[0014] The main circuit equivalent circuit is drawn by the following dynamic equation:

[0015]

[0016] Taking phase a as an example, the bridge arm current is represented by i ap Indicates that, where v ap 、v an is the sum of the upper and lower bridge arm capacitor voltages; C is the bridge arm equivalent capacitance, C = C SM / N;m ap 、m an is the switching coefficient of the upper and lower bridge arms, v dc is the DC side voltage, i jp 、i jn (j=a, b, c) are the three-phase upper and lower bridge arm currents, v sj is the three-phase AC side voltage, C SM is the submodule capacitance, L g and R g is the equivalent inductance and resistance of the power grid. Assume that the number of submodules N of the MMC is large, and then m ap 、m an It can be approximately continuously changed, so the a-phase equivalent circuit of MMC can be drawn by the dynamic equation.

[0017] Step 2) Set the bridge arm voltage v of the MMC p , bridge arm current i p The switching factor m in the modulation p The main variables are expressed as vectors in matrix form according to the frequencies corresponding to each harmonic.

[0018] Step 3) Calculate the steady-state harmonics in the frequency domain, which can be calculated as follows:

[0019]

[0020] Where the DC side voltage V dc , AC side phase voltage V s , bridge arm inductance admittance Y L , submodule capacitance impedance Z C is a known quantity, and the calculation including the third harmonic is considered, that is, n = 3, so the matrices in the steady-state frequency domain model are all seventh-order.

[0021] The DC component of the bridge arm current in the above formula is I p,0 , fundamental frequency component I p,1 , Y L and Z C The variables are

[0022]

[0023]

[0024] Considering the role of circulating current control, under ideal conditions, the double frequency component of the bridge arm current I p,2 is 0, the third harmonic component is zero sequence output, so I p,3 =0, the DC component of the switching factor M p,0 =0.5, select the rows of 0, ω0, 2ω0, 3ω0 with non-negative steady-state harmonic frequencies to form a matrix equation. The 7 unknown quantities are the capacitor voltage component V p,0 , V p,1 , V p,2 , V p,3 and the bridge arm current component I p,2 and the switching factor component M p,1 and M p,2 , write equations according to the MMC steady-state frequency domain model, remove one invalid equation, and solve all unknowns.

[0025] Step 4) Based on the equivalent circuit model, after adding disturbance to the DC port, a frequency domain linearization model of the main circuit is constructed;

[0026]

[0027] Where U is the unit matrix, the bridge arm current i p , bridge arm equivalent capacitance voltage v p , submodule switching coefficient m p Become The frequency corresponding to each row is added with the disturbance frequency ω r , becomes kω0+ω r .

[0028] The variables after adding disturbance are

[0029]

[0030] Step 5) constructing a small signal model of the control part based on the complete control structure;

[0031] When DC voltage and reactive power control is used Expressed as

[0032]

[0033] When active and reactive power control is used Expressed as

[0034]

[0035] The influence of the current inner loop embedded repetitive control on the switching coefficient in the above two equations is i as follows:

[0036]

[0037] Where k pi and k ii are the proportional and integral parameters of the current inner loop PI controller, K i is the current inner loop decoupling coefficient, k is the number of lead compensation beats, K r is the compensation gain, and N is the number of delay beats.

[0038] In the above formula, the definition of the switching function S 1k , S 2k as follows:

[0039]

[0040] The influence of the above active power control and reactive power control on the switching factor Δ P and Δ Q Determine using the following method:

[0041]

[0042] Where k pP and k iP , k pQ and k iQ denote the proportional and integral parameters of the active power and reactive power PI controllers respectively.

[0043] The influence of the above DC voltage outer loop control on the switching factor Δ v as follows:

[0044]

[0045] Where k pv and k ivThey represent the proportional and integral parameters of the DC voltage outer loop PI controller respectively.

[0046] The influence of the above circulation suppression on the switching coefficient Δ c Determine using the following method:

[0047]

[0048] Where k pc and k ic are the PI controller parameters for circulating current suppression, K c is the circulating current suppression decoupling coefficient.

[0049] Step 6) Based on the main circuit frequency domain linearization model and the control part small signal model, a modular multilevel converter DC port impedance modeling using an embedded repetitive controller is established;

[0050]

[0051] Where U represents the identity matrix, B i and B v and E i and E v is the coefficient matrix.

[0052] For UQ control, the coefficient matrix B described in the above formula is i and B v and E i and E v Expressed as

[0053]

[0054] For PQ control, the coefficient matrix B i and B v and E i Respectively expressed as

[0055]

[0056] E i =G ir (G Q V Q +G P V P )+G i +G c .

[0057] Y dc The reciprocal of the central element of is the impedance characteristic of the DC side, thus obtaining the DC impedance model based on the repetitive control structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1This is a schematic diagram of the three-phase MMC main circuit topology.

[0059] Figure 2 Schematic diagram of the overall control structure of MMC using an embedded repetitive controller.

[0060] Figure 3 This is the schematic diagram of the a-equal value circuit of the MMC system.

[0061] Figure 4 It is a schematic diagram comparing the theoretical results and simulation results of the impedance model of the present invention under PQ control.

[0062] Figure 5 It is a schematic diagram comparing the theoretical results and simulation results of the impedance model of the present invention under UQ control.

[0063] Figure 6 Flow chart for implementing the present invention. DETAILED DESCRIPTION

[0064] The present invention is further described below with reference to the accompanying drawings:

[0065] Figure 1 The topological structure diagram of the three-phase MMC main circuit is shown in Figure 2. The main circuit includes three-phase upper and lower bridge arms, each of which is composed of N sub-modules, bridge arm inductance L and resistance R in series. SM is the submodule capacitance, L g and R g is the equivalent inductance and resistance of the power grid. According to the topological structure, the dynamic equation of MMC is as follows:

[0066]

[0067] Among them, S jp,i , S jn,i (j=a, b, c) represents the switching state of the upper and lower bridge arms of the three-phase; v jp,i 、v jn,i Represents the i-th (0≤i≤N) capacitor voltage of the upper and lower bridge arms, v p 、v n Indicates the positive and negative voltages on the DC side, v j Represents the midpoint voltage of the bridge arm, and the complete double closed-loop control structure using the embedded repetitive controller is as follows Figure 2 shown.

[0068] The present invention provides a method for modeling the DC port impedance of an MMC using an embedded repetitive controller, characterized in that the method specifically comprises the following steps:

[0069] S1: Construct the equivalent circuit of the main circuit according to the mathematical model of MMC;

[0070] S2: Based on the modeling principle of multi-harmonic linearization, the MMC equivalent circuit is converted into the frequency domain and represented in the form of matrix and vector;

[0071] S3: simplifying the MMC frequency domain steady-state model, and calculating steady-state harmonics based on the model;

[0072] S4: Inject voltage disturbance into the DC port of the MMC to build a frequency domain linearization model of the main circuit under the action of the disturbance voltage;

[0073] S5: Based on the complete dual closed-loop control structure, a frequency domain model of the MMC control circuit is constructed;

[0074] S6: The frequency domain models of the main circuit and the control circuit are combined, and the calculation results of the steady-state harmonics are substituted into the frequency domain models, thereby obtaining the DC port impedance model of the MMC using the embedded repetitive controller;

[0075] The MMC DC port impedance modeling method using an embedded repetitive controller is characterized in that the circuit topology model is established in S1 as follows:

[0076]

[0077] Here we take phase a as an example, where v ap 、v an is the sum of the upper and lower bridge arm capacitor voltages, m ap 、m an is the switching coefficient of the upper and lower bridge arms, v dc is the DC side voltage, i jp 、i jn (j=a, b, c) are the three-phase upper and lower bridge arm currents, v sj (j=a,b,c) is the three-phase AC side voltage, and the bridge arm equivalent capacitance C=C SM / N, assuming that the number of sub-modules N of the MMC is large, and then m ap 、m an It can be approximated to change continuously, and thus the equivalent average model of the a phase of MMC is drawn as follows Figure 3 shown.

[0078] Taking the upper bridge arm variable during MMC steady-state operation as an example, the bridge arm voltage v p , bridge arm current i p The switching factor m in the modulation p The main variables are expressed as vectors consisting of the Fourier coefficients of the corresponding frequencies of each harmonic.

[0079]

[0080] Taking the third steady-state harmonic of the upper bridge arm voltage as an example, the Fourier coefficient is After normalization, each variable is input and the circuit topology model in S1 is converted to the frequency domain, as shown in the following formula. The multiplication operation between variables in the time domain becomes a convolution operation in the frequency domain.

[0081]

[0082] Where v dc represents the DC voltage vector, v s represents the AC port phase voltage vector, is the convolution operation.

[0083] The process of calculating steady-state harmonics is as follows. Considering the calculation including the third harmonic, that is, n=3, the matrices in the steady-state frequency domain model are all seventh-order.

[0084]

[0085] Where the DC side voltage V dc , AC side phase voltage V s , bridge arm inductance admittance Y L , submodule capacitance impedance Z C is a known quantity, and the DC component of the bridge arm current I p,0 and the fundamental frequency component I p,1 The following formula can be used for calculation:

[0086]

[0087] Ideally, due to the existence of circulating current suppression, the double frequency component of the bridge arm current I p,2 is 0, the third harmonic component is zero sequence output, so I p,3 =0, the DC component of the switching factor M p,0 =0.5, select the rows of 0, ω0, 2ω0, 3ω0 with non-negative steady-state harmonic frequencies to form a matrix equation, write the equation according to the MMC steady-state frequency domain model, and solve all the unknown capacitor voltage components V p,0 , V p,1 , V p,2 , V p,3 and the bridge arm current component I p,2 and the switching factor component M p,1 and M p,2 .

[0088] The diagonal matrix bridge arm inductance admittance Y L and submodule capacitance impedance Z C It can be expressed as:

[0089]

[0090] Taking the above bridge arm as an example, the vector with “^” in the formula represents the disturbance.

[0091]

[0092] The corresponding inductive admittance and capacitive impedance matrices become:

[0093]

[0094] Combining the equivalent circuit in the frequency domain and the above disturbance, the frequency domain linearization model of the MMC main circuit is expressed as:

[0095]

[0096] Where U is the unit matrix, the bridge arm current i p , bridge arm equivalent capacitance voltage v p , submodule switching coefficient m p Become The frequency corresponding to each row is added with the disturbance frequency ω r , becomes kω0+ω r .

[0097] The small signal model of the control part is calculated as follows:

[0098] When DC voltage and reactive power control is used Expressed as

[0099]

[0100] When active and reactive power control is used Expressed as

[0101]

[0102] The effects of the current inner loop embedded repetitive control, active power control, reactive power control, DC voltage outer loop control, and circulating current suppression on the switching coefficient are Δ i , Δ P , Δ Q , Δ v , Δ c .

[0103] Define the switching function to describe the phase sequence and phase classification:

[0104]

[0105] The influence of the current inner loop embedded repetitive control on the switching coefficient is determined by the following method:

[0106]

[0107] Where k pi and k ii are the proportional and integral parameters of the current inner loop PI controller, Ki is the current inner loop decoupling coefficient, k is the number of lead compensation beats, K r is the compensation gain, and N is the number of delay beats.

[0108] The influence of active power control and reactive power control on the switching coefficient is determined by the following method:

[0109]

[0110] Where k pP and k iP , k pQ and k iQ denote the proportional and integral parameters of the active power and reactive power PI controllers respectively.

[0111] The influence of the DC voltage outer loop control on the switching coefficient is determined by the following method:

[0112]

[0113] Where k pv and k iv They represent the proportional and integral parameters of the DC voltage outer loop PI controller respectively.

[0114] The influence of the circulating current suppression on the switching coefficient is determined by the following method:

[0115]

[0116] Where k pc and k ic are the PI controller parameters for circulating current suppression, K c is the circulating current suppression decoupling coefficient.

[0117] The DC side impedance can be expressed as

[0118]

[0119] Where U represents the identity matrix, B i and B v and E i and E v is the coefficient matrix.

[0120] For UQ control, the coefficient matrix B i and B v and E i and E v Expressed as

[0121]

[0122] For PQ control, the corresponding coefficient matrix B i and Bv and E i Respectively expressed as

[0123]

[0124] E i =G ir (G Q V Q +G P V P )+G i +G c .

[0125] Y dc The reciprocal of the central element of is the impedance characteristic of the DC side, thus obtaining the DC impedance model based on the repetitive control structure.

[0126] Build the main circuit in MATLAB / Simulink as follows Figure 1 The single-ended MMC system shown in Table 1 has simulation parameters. The comparison between the calculation results and simulation results of the MMC steady-state harmonics is shown in Table 2, where the capacitor voltage, bridge arm current and switching coefficient of the bridge arm on phase a are selected, and the calculation including the third harmonic is considered. It can be seen that the calculation results of the harmonics are consistent with the simulation results, which verifies the correctness of the frequency domain steady-state model of the present invention and provides a basis for the accurate establishment of the MMC impedance model. Figure 4 and Figure 5 The schematic diagrams are respectively comparative diagrams of the theoretical results and simulation results of the impedance model of the present invention under PQ control and UQ control. It can be seen that the simulation results are in good agreement with the theoretically derived impedance model, which verifies the correctness of the impedance model established by the present invention.

[0127] Table 1 Simulation parameters

[0128] variable Numeric variable Numeric <![CDATA[Rated AC side line voltage U g / kV]]> 290 Bridge arm inductance L / mH 75 <![CDATA[Rated capacity S N / MVA]]> 750 Bridge arm resistance R / ohm 0.1 <![CDATA[DC-side voltage v dc / kV]]> 500 <![CDATA[Sub-module capacitor C SM / mF]]> 15 Number of submodules N 244

[0129] Table 2 Steady-state harmonic calculation results

[0130]

[0131]

[0132] Note: The unit of voltage amplitude is kV, the unit of current amplitude is A, and the unit of phase is °.

[0133] The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A method for modeling the DC port impedance of an MMC using an embedded repetitive controller, characterized in that: The method specifically comprises the following steps: S1: Construct the equivalent circuit of the main circuit according to the mathematical model of MMC; S2: Based on the modeling principle of multi-harmonic linearization, the MMC equivalent circuit is converted into the frequency domain and represented in the form of matrix and vector; S3: simplifying the MMC frequency domain steady-state model, and calculating steady-state harmonics based on the model; S4: Inject voltage disturbance into the DC port of the MMC to build a frequency domain linearization model of the main circuit under the action of the disturbance voltage; S5: Based on the complete dual closed-loop control structure, a frequency domain model of the MMC control circuit is constructed; S6: The frequency domain models of the main circuit and the control circuit are combined, and the calculation results of the steady-state harmonics are substituted into the frequency domain models, thereby obtaining the DC port impedance model of the MMC using the embedded repetitive controller.

2. The MMC DC port impedance modeling method using an embedded repetitive controller according to claim 1, characterized in that: The main circuit equivalent circuit established in S1 is as follows: Here we take phase a as an example, where v ap 、v an is the sum of the upper and lower bridge arm capacitor voltages, C is the bridge arm equivalent capacitance, m ap 、m an is the switching coefficient of the upper and lower bridge arms, v dc is the DC side voltage, i jp 、i jn (j=a, b, c) are the three-phase upper and lower bridge arm currents, v sj (j=a,b,c) is the three-phase AC side voltage.

3. The MMC DC port impedance modeling method using an embedded repetitive controller according to claim 1, characterized in that: In S2, each system variable is represented as a vector consisting of the Fourier coefficients of the corresponding frequency of each harmonic, and the MMC time domain equivalent model is converted to the frequency domain and can be represented as: Among them, i p 、i n are the current vectors of the upper and lower bridge arms, v p 、v n are the upper and lower bridge arm capacitor voltage vectors, M p 、M n is the switching coefficient vector of the upper and lower bridge arms, v dc 、v s are the voltage vectors on the DC side and the AC side respectively, L and Z C are the diagonal matrix bridge arm inductance admittance and submodule capacitance impedance respectively.

4. The MMC DC port impedance modeling method using an embedded repetitive controller according to claim 1, characterized in that: In S3, the steady-state model is simplified by using the relationship between the upper and lower bridge arm variables and the Fourier coefficients corresponding to the negative frequencies in the vector are ignored, and the following matrix equation is obtained to solve the steady-state harmonics of the MMC: Wherein, the subscript n represents the harmonic order, I p,0 and I p,1 The relationship between the rated voltage and current on the DC side and the AC side can be used to solve the problem. Considering the suppression of circulating current, the double frequency component of the bridge arm current under ideal conditions is I p,2 =0, the third harmonic component is zero sequence output, so I p,3 =0, the DC component of the switching factor M p,0 =0.5; except for these known quantities, the remaining variables can be solved using independent equations.

5. The MMC DC port impedance modeling method using an embedded repetitive controller according to claim 1, characterized in that: The S4 injects a frequency of ω into the DC port of the MMC. r The disturbance voltage is used to construct the frequency domain model after the disturbance injection as follows: in, is the upper arm current disturbance, is the upper arm voltage disturbance, The upper arm switching coefficient disturbance, is a DC voltage disturbance. The frequency domain linearization model of the MMC main circuit is determined by the above formula:

6. The MMC DC port impedance modeling method using an embedded repetitive controller according to claim 1, characterized in that: In S5, a complete control circuit frequency domain model is constructed, and the switching coefficient disturbance Determine as follows: When DC voltage and reactive power control is used Expressed as When active and reactive power control is used Expressed as Among them, Δ i represents the effect of embedded repetitive control on the switching factor, Δ P Indicates the effect of active power on switching factor, Δ Q Indicates the effect of reactive power on the switching factor, Δ v Indicates the influence of DC voltage on the switching factor, Δ c Indicates the influence of circulating flow control on switching coefficient; The influence of the embedded repetitive control on the switching factor Δ i Determine as follows: in, is the AC current disturbance, G i is the transfer function matrix of the embedded repetitive controller, H i,k is the harmonic frequency ω r The transfer function of the embedded repetitive controller under +kω0, S 1,k and S 2,k Respectively represent the relationship between the three-phase variables and the upper and lower bridge arm variables; The influence of the DC voltage control on the switching factor Δ v Determine as follows: in, is the DC voltage disturbance, G ir is the transfer function matrix of the outer loop on the inner current loop, G v is the voltage outer loop transfer function matrix, H v,-1 is the harmonic frequency ω r Transfer function of voltage outer loop PI controller under -ω0; The influence of active and reactive power control on the switching factor Δ P and Δ Q Determine as follows: in, and are active and reactive power disturbances, G P and G Q are respectively the active and reactive power outer loop transfer function matrices, H P,-1 and H Q,-1 They are harmonic frequencies ω r Transfer functions of active outer loop and reactive outer loop PI controllers under -ω0; The influence of the circulating current suppression on the switching factor Δ c Determine as follows: in, is the circulation disturbance, G c is the transfer function matrix of circulating current suppression, H c,k is the harmonic frequency ω r Transfer function of the circulating current suppression PI controller at +kω0.

7. The MMC DC port impedance modeling method using an embedded repetitive controller according to claim 1, characterized in that: The frequency domain linearization model of the combined MMC and the switching coefficient disturbance in S6 The expression of DC current disturbance and DC voltage disturbance The ratio of the DC side admittance Y is as follows dc The expression is: Among them, U represents the identity matrix, B i and B v is the coefficient matrix; For UQ control, the coefficient matrix B i and B v Expressed as For PQ control, the coefficient matrix B i and B v Expressed as Y dc The reciprocal of the central element of is the impedance characteristic of the DC side. Substituting it into the calculation result of steady-state harmonics, the DC port impedance model of the MMC using an embedded repetitive controller is obtained.

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