A Modular Multilevel Converter AC Side Impedance Modeling Method

Abstract

The present invention discloses a method for modeling the AC-side impedance of a modular multilevel converter, which uses Fourier transform and Euler's formula to obtain the arm current in phasor form, the equivalent capacitor voltage of the arm, and the sub-module switching coefficient; according to the arm current, the equivalent capacitor voltage of the arm, the sub-module switching coefficient, and the average value mathematical model of the MMC in the time domain, the steady-state frequency-domain model of the MMC is obtained; according to the method of harmonic linearization, a voltage perturbation signal with a frequency of f s is injected at the point of common coupling of the steady-state frequency-domain model, and the steady-state frequency-domain model is linearized at the steady-state operating point to obtain the small-signal frequency-domain model of the MMC main circuit after the perturbation is injected; according to the control system of the MMC, each control link is modeled respectively to obtain the small-signal model of the sub-module switching coefficient after the perturbation is injected; according to the small-signal frequency-domain model of the MMC main circuit and the small-signal model of the sub-module switching coefficient, the AC-side impedance of the MMC is solved, realizing more accurate impedance modeling of the MMC.

Description

Technical Field

[0001] The present invention relates to the technical field of flexible direct current power transmission systems, and in particular to a modular multi-level converter alternating current side impedance modeling method. Background Art

[0002] In recent years, flexible direct current transmission technology has been widely used in power transmission systems due to its advantages of high controllability, low harmonic content, and flexible structure. With the increasing number of flexible direct current transmission projects, flexible direct current transmission technology based on modular multilevel converter (MMC) has developed rapidly in the fields of new energy access and asynchronous grid interconnection. Flexible direct current grids have the characteristics of nonlinearity and strong coupling, so MMC converter stations are easily affected by harmonics, which in turn causes resonance of the entire direct current system. At present, many MMC-HVDC systems have experienced oscillation during operation or commissioning. In-depth and comprehensive analysis of the MMC oscillation mechanism is of great significance to ensure the safe and stable operation of the power grid.

[0003] At present, the academic community mainly uses the frequency domain analysis method based on impedance modeling to study the broadband oscillation problem of power electronic interconnection system, and it has been widely used in the inverter grid-connected system. Considering the harmonic interaction coupling characteristics of the bridge arm current and capacitor voltage inside the MMC and the inherent nonlinear characteristics of the MMC control system, it is very difficult to accurately model the impedance of the MMC. At present, the MMC impedance model established in most literature ignores the frequency coupling effect of multiple electrical variables inside the MMC, or the established model only considers the relatively simple AC voltage outer loop control or even ignores the asymmetric control outer loop. The MMC impedance model obtained based on the above assumptions may cause inaccurate analysis results when conducting system stability research. Therefore, it is necessary to consider the internal electrical quantities of the MMC and the coupling characteristics of the internal and external loop control to establish a more accurate MMC impedance model. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a modular multi-level converter AC side impedance modeling method to achieve more accurate MMC impedance modeling.

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

[0006] A modular multi-level converter AC side impedance modeling method comprises the steps of:

[0007] S1, using Fourier transform and Euler formula to convert the bridge arm current i of MMC u , bridge arm equivalent capacitance voltage v u and submodule switching factor s u Converted to the frequency domain, the bridge arm current i is obtained in phasor formu , bridge arm equivalent capacitance voltage v u and submodule switching factor s u ;

[0008] S2, according to the bridge arm current i u , the bridge arm equivalent capacitance voltage v u , the submodule switching coefficient s u and the average value mathematical model of MMC in the time domain to obtain the steady-state frequency domain model of MMC;

[0009] S3, according to the harmonic linearization method, the injection frequency is f at the common connection point of the steady-state frequency domain model. s The voltage disturbance signal The steady-state frequency domain model is linearized at the steady-state operating point to obtain a frequency domain small signal model of the MMC main circuit after the disturbance is injected;

[0010] S4. Model each control link according to the MMC control system to obtain the small signal model of the submodule switching coefficient after the disturbance is injected.

[0011] S5. According to the frequency domain small signal model of the MMC main circuit and the small signal model of the submodule switching coefficient, solve the AC side impedance Z of the MMC MMC_AC (f s ).

[0012] In order to solve the above technical problems, another technical solution adopted by the present invention is:

[0013] A modular multilevel converter AC side impedance modeling terminal comprises a processor, a memory and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps in the above modular multilevel converter AC side impedance modeling method are implemented.

[0014] The beneficial effects of the present invention are as follows: a modular multi-level converter AC side impedance modeling method of the present invention takes into account the mutual coupling of multiple electrical harmonic variables inside the MMC, including bridge arm current, capacitor voltage, etc., and the influence caused by various links of the control system, so as to achieve more accurate MMC impedance modeling, provide a theoretical basis for studying the operating stability of the MMC-HVDC system, and provide a reference for the design of MMC control strategy and control parameter setting. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 A flowchart of a modular multi-level converter AC side impedance modeling method according to an embodiment of the present invention;

[0016] Figure 2A structural diagram of a modular multi-level converter AC side impedance modeling terminal according to an embodiment of the present invention;

[0017] Figure 3 A schematic diagram of an MMC average value equivalent model of a modular multilevel converter AC side impedance modeling method according to an embodiment of the present invention;

[0018] Figure 4 A schematic diagram of harmonic disturbance injection at the MMC AC side of a modular multilevel converter AC side impedance modeling method according to an embodiment of the present invention;

[0019] Figure 5 It is a block diagram of an MMC control system of a modular multi-level converter AC side impedance modeling method according to an embodiment of the present invention;

[0020] Figure 6 A schematic diagram of an MMC harmonic component path of a modular multilevel converter AC side impedance modeling method according to an embodiment of the present invention;

[0021] Figure 7 An MMC DC side equivalent circuit diagram of a modular multilevel converter AC side impedance modeling method according to an embodiment of the present invention;

[0022] Figure 8 A schematic diagram of comparing AC side impedance curves of MMC using different control modes in a modular multilevel converter AC side impedance modeling method according to an embodiment of the present invention;

[0023] Fig. 9 A schematic diagram of the impedance of an MMC interconnection system using different control link delays in a modular multilevel converter AC side impedance modeling method according to an embodiment of the present invention;

[0024] Fig.10 A schematic diagram of a three-phase voltage simulation waveform on the AC side of a modular multi-level converter AC side impedance modeling method according to an embodiment of the present invention;

[0025] Fig.11 A schematic diagram of an AC side A phase voltage FFT analysis result of a modular multilevel converter AC side impedance modeling method according to an embodiment of the present invention;

[0026] Description of labels:

[0027] 1. A modular multi-level converter AC side impedance modeling terminal; 2. A processor; 3. A memory. DETAILED DESCRIPTION

[0028] In order to explain the technical content, achieved objectives and effects of the present invention in detail, the following is an explanation in conjunction with the implementation modes and the accompanying drawings.

[0029] Please refer to Figure 1 and 3 to Figure 7 , a modular multi-level converter AC side impedance modeling method, comprising the steps of:

[0030] S1, using Fourier transform and Euler formula to convert the bridge arm current i of MMC u , bridge arm equivalent capacitance voltage v u and submodule switching factor s u Converted to the frequency domain, the bridge arm current i is obtained in phasor form u , bridge arm equivalent capacitance voltage v u and submodule switching factor s u ;

[0031] S2, according to the bridge arm current i u , the bridge arm equivalent capacitance voltage v u , the submodule switching coefficient s u and the average value mathematical model of MMC in the time domain to obtain the steady-state frequency domain model of MMC;

[0032] S3, according to the harmonic linearization method, the injection frequency is f at the common connection point of the steady-state frequency domain model. s The voltage disturbance signal The steady-state frequency domain model is linearized at the steady-state operating point to obtain a frequency domain small signal model of the MMC main circuit after the disturbance is injected;

[0033] S4. Model each control link according to the MMC control system to obtain the small signal model of the submodule switching coefficient after the disturbance is injected.

[0034] S5. According to the frequency domain small signal model of the MMC main circuit and the small signal model of the submodule switching coefficient, solve the AC side impedance Z of the MMC MMC_AC (f s ).

[0035] From the above description, it can be seen that the beneficial effects of the present invention are: a modular multi-level converter AC side impedance modeling method of the present invention takes into account the mutual coupling of multiple electrical harmonic variables inside the MMC, including bridge arm current, capacitor voltage, etc., and the influence caused by various links of the control system, so as to achieve more accurate MMC impedance modeling, provide a theoretical basis for studying the operation stability of the MMC-HVDC system, and provide a reference for the design of MMC control strategy and control parameter setting.

[0036] Furthermore, the step S1 specifically includes:

[0037] S11, according to Fourier transform, the bridge arm current i of MMC u Decomposed into DC component and sinusoidal signals of different frequencies:

[0038]

[0039] Among them, I0 is the DC component of the MMC bridge arm current, I n is the amplitude of the nth harmonic component of the MMC bridge arm current, α n Indicates the phase of the nth harmonic component of the MMC bridge arm current;

[0040] S12, according to Euler's formula, the bridge arm current i of the MMC u Convert to exponential form:

[0041]

[0042] Wherein, j represents the imaginary unit;

[0043] S13, use the same method to set the bridge arm equivalent capacitor voltage v u , submodule switching coefficient s u Converted to the frequency domain, the bridge arm current i is obtained in phasor form u , bridge arm equivalent capacitance voltage v u , submodule switching coefficient s u :

[0044]

[0045]

[0046]

[0047] Among them, each element in the formula corresponds to the harmonic components with frequencies from -nf1 to nf1, f1 represents the fundamental frequency, V n Represents the equivalent capacitance voltage of the MMC bridge arm, S n Indicates the amplitude of the nth harmonic component of the submodule switching coefficient, α n Indicates the phase of the nth harmonic component of the MMC bridge arm current, β n Indicates the phase of the nth harmonic component of the equivalent capacitor voltage of the MMC bridge arm, γ n Indicates the phase of the nth harmonic component of the submodule switching coefficient.

[0048] From the above description, it can be seen that the present invention uses the above formula to convert the bridge arm current i of the MMC u , bridge arm equivalent capacitance voltage v u , submodule switching coefficient s u Converted to the frequency domain, the bridge arm current i is obtained in phasor form u , bridge arm equivalent capacitance voltage v u , submodule switching coefficient s u .

[0049] Furthermore, the step S2 specifically includes:

[0050] S21, the bridge arm current i of MMC u , bridge arm equivalent capacitance voltage v u , submodule switching coefficient s u Substituting the average value mathematical model in the MMC time domain into the frequency domain convolution operation instead of the product operation in the time domain, we can get:

[0051]

[0052]

[0053] Among them, V dc represents the DC voltage phasor, u v Indicates the AC side voltage phasor, U dc is the DC side voltage of MMC, V s and are the voltage amplitude and phase angle of the MMC AC side, Y L The admittance matrix of the bridge arm reactance, Z C The impedance matrix representing the equivalent capacitance of the bridge arm, R0 is the equivalent resistance of the MMC bridge arm, L0 is the equivalent reactance of the MMC bridge arm, and C0 is the equivalent capacitance of the MMC bridge arm;

[0054] S22. Using the Toeplitz matrix, the phasor convolution operation is converted into a dot product operation between the matrix and the phasor, and the steady-state frequency domain model of the MMC is obtained:

[0055]

[0056] Among them, S u is the submodule switching factor s u The Toeplitz matrix form can be expressed as:

[0057]

[0058] Among them, S n represents the amplitude of the harmonic component of the switching coefficient of the submodule, j represents the imaginary unit, γ n Indicates the phase of the nth harmonic component of the submodule switching coefficient.

[0059] From the above description, it can be seen that the present invention converts the bridge arm current i in phasor form u , bridge arm equivalent capacitance voltage v u , submodule switching coefficient s u Substitute the average value mathematical model of MMC in the time domain and complete the transformation of MMC from the time domain model to the steady-state frequency domain model according to the above formula.

[0060] Furthermore, the step S3 specifically includes:

[0061] S31, injection frequency f at the common connection point s The voltage disturbance signal The bridge arm current of the MMC after the disturbance injection can be obtained Bridge arm equivalent capacitance voltage Submodule switching factor

[0062]

[0063] Among them, ^ represents the small signal variable corresponding to each variable;

[0064] S32, inject the bridge arm current of the MMC after the disturbance Bridge arm equivalent capacitance voltage Submodule switching factor Substitute it into the steady-state frequency domain model of MMC and linearize it at the steady-state operating point to obtain the frequency domain small signal model of the MMC main circuit after the disturbance is injected:

[0065]

[0066] in, is the phase angle of the injected disturbance voltage signal, Y Ls It represents the admittance matrix of the bridge arm reactance after the disturbance is injected, Z Cs The impedance matrix of the equivalent capacitance of the bridge arm after the disturbance is injected, V u and I u They are the equivalent capacitance voltage v of the MMC bridge arm respectively u , bridge arm current i u The Toeplitz matrix form can be expressed as:

[0067]

[0068] Where j represents the imaginary unit, I n is the amplitude of the nth harmonic component of the MMC bridge arm current, V n Represents the equivalent capacitance voltage of the MMC bridge arm, α n Indicates the phase of the nth harmonic component of the MMC bridge arm current, β n Indicates the phase of the nth harmonic component of the MMC bridge arm equivalent capacitor voltage.

[0069] From the above description, it can be seen that the harmonic linearization method is used to inject a frequency of f at the common connection point (PCC) s The voltage disturbance signal The above formula is used to linearize the steady-state frequency domain model of the MMC at the steady-state operating point, and the frequency domain small signal model of the MMC main circuit after the disturbance is injected is obtained.

[0070] Furthermore, the step S4 specifically includes:

[0071] S41. Classify the internal harmonic phase sequence and phase of the MMC. The classification function is:

[0072]

[0073] Where k represents the harmonic order, A k and are the classification functions of output components and circulation components, A k =1 means that the harmonic is the output component, A k =0 means that the harmonic is the circulating current component. Indicates that this harmonic is the circulating current component. Indicates that this harmonic is the output component, B k is the classification function of positive sequence component, negative sequence component and zero sequence component, B k =1 means that the harmonic is a positive sequence component, B k =-1 means that the harmonic is a positive sequence component, B k =0 means that the harmonic is a zero-sequence component;

[0074] S42, consider the current control inner loop to the MMC submodule switching coefficient The influence of the current control inner loop on the bridge arm current The control function G i for:

[0075]

[0076] Where f1 represents the fundamental frequency, f s Represents the frequency of the voltage disturbance signal, H i represents the current inner loop transfer function, K ip and K ii are the proportional coefficient and integral coefficient of the current inner loop PI controller, j represents the imaginary unit, and L0 is the equivalent reactance of the MMC bridge arm;

[0077] S43, considering the circulation suppression link to the MMC submodule switching coefficient The influence of the circulating current suppression link on the bridge arm current The control function G cir for:

[0078]

[0079] Among them, H c represents the transfer function of the circulating current suppression link, K cirp and K ciriThey are the proportional coefficient and integral coefficient of the PI controller in the circulating current suppression link respectively;

[0080] S44, consider the DC voltage outer loop control link to the MMC sub-module switching coefficient The influence of DC voltage disturbance for:

[0081]

[0082] The DC voltage outer loop control link affects the DC voltage disturbance The control function G Vdc for:

[0083]

[0084] Among them, Z dcs is the equivalent impedance of the MMC DC side after the disturbance is injected, G dc represents the DC voltage outer loop control function, G ir represents the current inner loop forward path control function, H dc represents the DC voltage outer loop transfer function, K dcp and K dci are the proportional coefficient and integral coefficient of the DC voltage outer loop PI controller respectively;

[0085] S45, considering the active power outer loop control link and the reactive power outer loop control link to the MMC submodule switching coefficient The influence of active power disturbance and reactive power disturbance They are:

[0086]

[0087]

[0088]

[0089] If the power outer loop control adopts active power control, the power outer loop control link will affect the active power disturbance The control function G OP for:

[0090]

[0091] If the power outer loop control adopts reactive power control, the power outer loop control link will affect the reactive power disturbance The control function G OQ for:

[0092]

[0093] Among them, G P represents the active power outer loop control function, H P represents the active power outer loop transfer function, K Pp and K Pi are the proportional coefficient and integral coefficient of the active power outer loop PI controller, G Q represents the reactive power outer loop control function, H Q represents the reactive power outer loop transfer function, K Qp and K Qi are the proportional coefficient and integral coefficient of the reactive power outer loop PI controller, Represents voltage disturbance signal;

[0094] S46. For the MMC control system using DC voltage control and reactive power control, the small signal model of the submodule switching coefficient is obtained after injecting disturbance for:

[0095]

[0096] For the MMC control system using active power control and reactive power control, the small signal model of the submodule switching coefficient is obtained after injecting disturbance: for:

[0097]

[0098] Among them, T d To control link delay.

[0099] From the above description, it can be seen that in order to obtain the MMC AC side impedance model, it is necessary to eliminate the submodule switching coefficient in the MMC main circuit frequency domain small signal model. Therefore, it is necessary to model the MMC control system to obtain the submodule switching coefficient With voltage disturbance signal Bridge arm current Therefore, according to the above steps, each control link of MMC is modeled. Among them, the internal harmonic phase sequence and phase of MMC are classified to facilitate the subsequent modeling of each control link.

[0100] Furthermore, the step S5 specifically includes:

[0101] S51, small signal model of the switching coefficient of the submodule after the disturbance is injected Substituting into the frequency domain small signal model of the MMC main circuit, the MMC AC side admittance Y is obtained:

[0102]

[0103]

[0104]

[0105] Among them, E is the identity matrix, A i , A v 、M i and M v are all intermediate variables. represents the bridge arm current of the MMC after the disturbance is injected, T d To control link delay, Represents the voltage disturbance signal, Y Ls It represents the admittance matrix of the bridge arm reactance after the disturbance is injected, Z Cs The impedance matrix of the equivalent capacitance of the bridge arm after the disturbance is injected, V u and I u They are the equivalent capacitance voltage v of the MMC bridge arm respectively u , bridge arm current i u The Toeplitz matrix form, S u is the submodule switching factor s u Toeplitz matrix form of ;

[0106] S52, calculating the AC side impedance Z according to the AC side admittance Y MMC_AC (f s ):

[0107]

[0108] From the above description, we can know that the small signal model of the switching coefficient of the submodule after the disturbance is injected Substituting into the frequency domain small signal model of the MMC main circuit, the MMC AC side admittance Y can be obtained according to the above formula, and the MMC AC side impedance Z can be calculated MMC_AC (f s ).

[0109] Please refer to Figure 2 A modular multilevel converter AC side impedance modeling terminal comprises a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps in the above modular multilevel converter AC side impedance modeling method are implemented.

[0110] A modular multilevel converter AC side impedance modeling method of the present invention is suitable for scenarios where impedance modeling is required in related research on flexible direct current transmission technology of modular multilevel converters.

[0111] Please refer to Figure 1 as well as Figures 3 to 11 , Embodiment 1 of the present invention is:

[0112] A modular multi-level converter AC side impedance modeling method comprises the steps of:

[0113] S1, using Fourier transform and Euler formula to convert the bridge arm current i of MMC u , bridge arm equivalent capacitance voltage v u and submodule switching factor s u Converted to the frequency domain, the bridge arm current i is obtained in phasor form u , bridge arm equivalent capacitance voltage v u and submodule switching factor s u ;

[0114] The step S1 specifically includes:

[0115] S11, according to Fourier transform, the bridge arm current i of MMC u Decomposed into DC component and sinusoidal signals of different frequencies:

[0116]

[0117] Among them, I0 is the DC component of the MMC bridge arm current, I n is the amplitude of the nth harmonic component of the MMC bridge arm current, α n Indicates the phase of the nth harmonic component of the MMC bridge arm current;

[0118] S12, according to Euler's formula, the bridge arm current i of the MMC u Convert to exponential form:

[0119]

[0120] Wherein, j represents the imaginary unit;

[0121] S13, use the same method to set the bridge arm equivalent capacitor voltage v u , submodule switching coefficient s u Converted to the frequency domain, the bridge arm current i is obtained in phasor form u , bridge arm equivalent capacitance voltage v u , submodule switching coefficient s u :

[0122]

[0123]

[0124]

[0125] Among them, each element in the formula corresponds to the harmonic components with frequencies from -nf1 to nf1, f1 represents the fundamental frequency, V n Represents the equivalent capacitance voltage of the MMC bridge arm, Sn Indicates the amplitude of the nth harmonic component of the submodule switching coefficient, α n Indicates the phase of the nth harmonic component of the MMC bridge arm current, β n Indicates the phase of the nth harmonic component of the equivalent capacitor voltage of the MMC bridge arm, γ n Indicates the phase of the nth harmonic component of the submodule switching coefficient.

[0126] In this embodiment, based on Figure 3 The average value equivalent model of MMC is constructed by using equations (1) to (3) to convert the bridge arm current i of MMC into u , bridge arm equivalent capacitance voltage v u , submodule switching coefficient s u Converted to the frequency domain, the bridge arm current i is obtained in phasor form u , bridge arm equivalent capacitance voltage v u , submodule switching coefficient s u .

[0127] S2, according to the bridge arm current i u , the bridge arm equivalent capacitance voltage v u , the submodule switching coefficient s u and the average value mathematical model of MMC in the time domain to obtain the steady-state frequency domain model of MMC;

[0128] The step S2 specifically includes:

[0129] S21, the bridge arm current i of MMC u , bridge arm equivalent capacitance voltage v u , submodule switching coefficient s u Substituting the average value mathematical model in the MMC time domain into the frequency domain convolution operation instead of the product operation in the time domain, we can get:

[0130]

[0131]

[0132] Among them, V dc represents the DC voltage phasor, u v Indicates the AC side voltage phasor, U dc is the DC side voltage of MMC, V s and are the voltage amplitude and phase angle of the MMC AC side, Y L The admittance matrix of the bridge arm reactance, Z C The impedance matrix representing the equivalent capacitance of the bridge arm, R0 is the equivalent resistance of the MMC bridge arm, L0 is the equivalent reactance of the MMC bridge arm, and C0 is the equivalent capacitance of the MMC bridge arm;

[0133] S22. Using the Toeplitz matrix, the phasor convolution operation is converted into a dot product operation between the matrix and the phasor, and the steady-state frequency domain model of the MMC is obtained:

[0134]

[0135] Among them, S u is the submodule switching factor s u The Toeplitz matrix form can be expressed as:

[0136]

[0137] Among them, S n represents the amplitude of the harmonic component of the switching coefficient of the submodule, j represents the imaginary unit, γ n Indicates the phase of the nth harmonic component of the submodule switching coefficient.

[0138] In this embodiment, the bridge arm current i in phasor form is u , bridge arm equivalent capacitance voltage v u , submodule switching coefficient s u Substitute the average value mathematical model of MMC in the time domain and use equations (4) to (5) to complete the transformation of MMC from the time domain model to the steady-state frequency domain model.

[0139] S3, according to the harmonic linearization method, the injection frequency is f at the common connection point of the steady-state frequency domain model. s The voltage disturbance signal The steady-state frequency domain model is linearized at the steady-state operating point to obtain a frequency domain small signal model of the MMC main circuit after the disturbance is injected;

[0140] The step S3 specifically includes:

[0141] S31, injection frequency f at the common connection point s The voltage disturbance signal The bridge arm current of the MMC after the disturbance injection can be obtained Bridge arm equivalent capacitance voltage Submodule switching factor

[0142]

[0143] Among them, ^ represents the small signal variable corresponding to each variable;

[0144] S32, inject the bridge arm current of the MMC after the disturbance Bridge arm equivalent capacitance voltage Submodule switching factor Substitute it into the steady-state frequency domain model of MMC and linearize it at the steady-state operating point to obtain the frequency domain small signal model of the MMC main circuit after the disturbance is injected:

[0145]

[0146] in, is the phase angle of the injected disturbance voltage signal, Y Ls It represents the admittance matrix of the bridge arm reactance after the disturbance is injected, Z Cs The impedance matrix of the equivalent capacitance of the bridge arm after the disturbance is injected, V u and I u They are the equivalent capacitance voltage v of the MMC bridge arm respectively u , bridge arm current i u The Toeplitz matrix form can be expressed as:

[0147]

[0148] Where j represents the imaginary unit, I n is the amplitude of the nth harmonic component of the MMC bridge arm current, V n Represents the equivalent capacitance voltage of the MMC bridge arm, α n Indicates the phase of the nth harmonic component of the MMC bridge arm current, β n Indicates the phase of the nth harmonic component of the MMC bridge arm equivalent capacitor voltage.

[0149] In this embodiment, according to Figure 5 Schematic diagram of harmonic disturbance injection on the AC side of MMC. The harmonic linearization method is used to inject a frequency of f at the common connection point (PCC). s The voltage disturbance signal The steady-state frequency domain model of the MMC is linearized at the steady-state operating point using equations (6) and (7), and the frequency domain small signal model of the MMC main circuit after the disturbance is injected is obtained.

[0150] S4. Model each control link according to the MMC control system to obtain the small signal model of the submodule switching coefficient after the disturbance is injected.

[0151] In this embodiment, in order to obtain the MMC AC side impedance model, it is necessary to eliminate the submodule switching coefficient in the MMC main circuit frequency domain small signal model. Therefore, it is necessary to model the MMC control system to obtain the submodule switching coefficient With voltage disturbance signal Bridge arm current According to Figure 2 The MMC control block diagram shown models each control link of the MMC.

[0152] The step S4 specifically includes:

[0153] S41. Classify the internal harmonic phase sequence and phase of the MMC. The classification function is:

[0154]

[0155] Where k represents the harmonic order, A k and are the classification functions of output components and circulation components, A k =1 means that the harmonic is the output component, A k =0 means that the harmonic is the circulating current component. Indicates that this harmonic is the circulating current component. Indicates that this harmonic is the output component, B k is the classification function of positive sequence component, negative sequence component and zero sequence component, B k =1 means that the harmonic is a positive sequence component, B k =-1 means that the harmonic is a positive sequence component, B k =0 means that the harmonic is a zero-sequence component.

[0156] In this embodiment, according to Figure 6 Due to the differences in the phase sequence and phase of the internal harmonics of the MMC, the harmonics flowing through the DC side, AC side and the internal circulating current of the MMC are different, and the harmonics flowing through each control link are also different. Therefore, formula (8) is used to classify the phase sequence and phase of the internal harmonics of the MMC, so as to facilitate the subsequent modeling of each control link.

[0157] S42, consider the current control inner loop to the MMC submodule switching coefficient The influence of the current control inner loop on the bridge arm current The control function G i for:

[0158]

[0159] Among them, H i represents the current inner loop transfer function, K ip and K ii They are the proportional coefficient and integral coefficient of the current inner loop PI controller respectively;

[0160] S43, considering the circulation suppression link to the MMC submodule switching coefficient The influence of the circulating current suppression link on the bridge arm current The control function G cir for:

[0161]

[0162] Among them, H c represents the transfer function of the circulating current suppression link, K cirp and K ciri They are respectively the proportional coefficient and integral coefficient of the PI controller in the circulating current suppression link.

[0163] In this embodiment, according to Figure 4 The control structure of the current control inner loop and the circulating current suppression link shown in FIG. 1 is used to obtain the effect of the current control inner loop and the circulating current suppression link on the bridge arm current according to equations (9) and (10). The control function G i With G cir .

[0164] S44, consider the DC voltage outer loop control link to the MMC sub-module switching coefficient The influence of DC voltage disturbance for:

[0165]

[0166] The DC voltage outer loop control link affects the DC voltage disturbance The control function G Vdc for:

[0167]

[0168] Among them, Z dcs is the equivalent impedance of the MMC DC side after the disturbance is injected, G dc represents the DC voltage outer loop control function, G ir represents the current inner loop forward path control function, H dc represents the DC voltage outer loop transfer function, K dcp and K dci They are the proportional coefficient and integral coefficient of the DC voltage outer loop PI controller respectively.

[0169] In this embodiment, according to Figure 7 The equivalent circuit diagram of the MMC DC side is shown in the figure. The MMC DC side can be equivalent to the Norton equivalent model of the current source parallel impedance. When the MMC is in symmetrical operation, only the zero-sequence circulating current component of the bridge arm current flows through the DC side, and this current is evenly divided among the three phases. Therefore, the DC voltage disturbance can be obtained from formula (11): With bridge arm current According to formula (12), the DC voltage outer loop control link can be used to obtain the DC voltage disturbance The control function G Vdc .

[0170] S45, considering the active power outer loop control link and the reactive power outer loop control link to the MMC submodule switching coefficient The influence of active power disturbance and reactive power disturbance They are:

[0171]

[0172]

[0173]

[0174] If the power outer loop control adopts active power control, the power outer loop control link will affect the active power disturbance The control function G OP for:

[0175]

[0176] If the power outer loop control adopts reactive power control, the power outer loop control link will affect the reactive power disturbance The control function G OQ for:

[0177]

[0178] Among them, G P represents the active power outer loop control function, H P represents the active power outer loop transfer function, K Pp and K Pi are the proportional coefficient and integral coefficient of the active power outer loop PI controller, G Q represents the reactive power outer loop control function, H Q represents the reactive power outer loop transfer function, K Qp and K Qi They are the proportional coefficient and integral coefficient of the reactive power outer loop PI controller respectively.

[0179] In this embodiment, the active power disturbance can be obtained from formula (13): and reactive power disturbance Establish its relationship with the voltage disturbance signal Bridge arm current According to equations (14) and (15), the power outer loop control link can be used to obtain the active power disturbance Reactive power disturbance The control function G OP With G OQ .

[0180] S46. For the MMC control system using DC voltage control and reactive power control, the small signal model of the submodule switching coefficient is obtained after injecting disturbance for:

[0181]

[0182] For the MMC control system using active power control and reactive power control, the small signal model of the submodule switching coefficient is obtained after injecting disturbance: for:

[0183]

[0184] Among them, T d To control link delay.

[0185] In this embodiment, the previous parts are added according to the different control methods adopted by the control link, and the small signal model of the submodule switching coefficient after the disturbance is injected is obtained according to equations (16) and (17):

[0186] S5. According to the frequency domain small signal model of the MMC main circuit and the small signal model of the submodule switching coefficient, solve the AC side impedance Z of the MMC MMC_AC (f s );

[0187] The step S5 specifically includes:

[0188] S51, small signal model of the switching coefficient of the submodule after the disturbance is injected Substituting into the frequency domain small signal model of the MMC main circuit, the MMC AC side admittance Y is obtained:

[0189]

[0190] in:

[0191]

[0192]

[0193] Among them, E is the identity matrix, A i , A v 、M i and M v are all intermediate variables. represents the bridge arm current of the MMC after the disturbance is injected, T d To control link delay, Represents the voltage disturbance signal, Y Ls It represents the admittance matrix of the bridge arm reactance after the disturbance is injected, Z Cs The impedance matrix of the equivalent capacitance of the bridge arm after the disturbance is injected, V u and I u They are the equivalent capacitance voltage v of the MMC bridge arm respectively u , bridge arm current iu The Toeplitz matrix form, S u is the submodule switching factor s u Toeplitz matrix form of ;

[0194] S52, calculating the AC side impedance Z according to the AC side admittance Y MMC_AC (f s ):

[0195]

[0196] In this embodiment, the small signal model of the switching coefficient of the submodule after the disturbance is injected Substituting into the frequency domain small signal model of the MMC main circuit, the MMC AC side admittance Y can be obtained according to formula (18), and then the MMC AC side impedance Z can be calculated according to formula (19): MMC_AC (f s ).

[0197] The present invention uses the harmonic injection method to conduct comparative verification on Matlab programming and PSCAD / EMTDC platform. Figure 8 This is a comparison diagram of the AC side impedance of MMC using different control methods. The solid line and circle represent the analytical calculation results and simulation sweep results of MMC using constant DC voltage control and constant reactive power control, respectively. The dotted line and square represent the analytical calculation results and simulation sweep results of MMC using constant active power control and constant reactive power control, respectively. It can be seen that the programming calculation results and the sweep results are almost the same, which verifies the accuracy of the proposed modeling method. At the same time, it can be proved that different control methods of MMC will affect the frequency characteristics of MMC.

[0198] like Fig. 9 The impedance diagram of the MMC interconnected system with different control link delays is shown in the figure. The dotted line is the impedance characteristic of the AC system. The dotted line indicates that the MMC uses a 200us control link delay, and the solid line indicates that the MMC uses a 500us control link delay. From the figure, it can be seen that the impedance characteristics of the MMC and the AC system have an amplitude intersection at 1146.3Hz, with a phase difference of 189.14°, and the corresponding phase margin is -9.14°. In theory, high-frequency oscillation will occur when the system becomes unstable. Fig.10 As shown in the simulation waveform of the AC side voltage, when t = 1.5s, the MMC control link delay is increased from 200us to 500us. From the waveform shown in the figure, it can be found that the three-phase voltage on the AC side has high-frequency oscillation, such as Fig.11 The FFT analysis results of the AC side A phase voltage shown in the figure show that the high-frequency harmonic component with a frequency of 1150 Hz appears in the voltage, which is consistent with the theoretical analysis results and further proves the effectiveness of the proposed MMC impedance model.

[0199] Please refer to Figure 2 , Embodiment 2 of the present invention is:

[0200] A modular multilevel converter AC side impedance modeling terminal 1 comprises a processor 2, a memory 3, and a computer program stored in the memory 3 and executable on the processor 2. When the processor 2 executes the computer program, the steps of a modular multilevel converter AC side impedance modeling method in the first embodiment are implemented.

[0201] In summary, the modular multilevel converter AC side impedance modeling method provided by the present invention takes into account the mutual coupling of multiple electrical harmonic variables inside the MMC, including bridge arm current, capacitor voltage, etc., as well as the influence caused by various links of the control system, to achieve more accurate MMC impedance modeling, and provides a theoretical basis for studying the operation stability of the MMC-HVDC system, and provides a reference for the design of MMC control strategies and control parameter setting, and can be used to analyze the influence of various control links of the MMC and control link delay and other parameters on its frequency characteristics.

[0202] The above descriptions are merely embodiments of the present invention and are not intended to limit the patent scope of the present invention. Any equivalent transformations made using the contents of the present invention's specification and drawings, or directly or indirectly applied in related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A modular multi-level converter AC side impedance modeling method, characterized in that: Includes steps: S1. Use Fourier transform and Euler formula to convert the bridge arm current of MMC i u , bridge arm equivalent capacitance voltage v u and submodule switching factor s u Converted to the frequency domain, the bridge arm current is obtained in phasor form , bridge arm equivalent capacitance voltage and submodule switching factor ; The step S1 specifically includes: S11, according to Fourier transform, the bridge arm current of MMC i u Decomposed into DC component and sinusoidal signals of different frequencies: ； in, is the DC component of the MMC bridge arm current, is the amplitude of the nth harmonic component of the MMC bridge arm current, Indicates the phase of the nth harmonic component of the MMC bridge arm current; S12, according to Euler's formula, the bridge arm current of MMC i u Convert to exponential form: ； Wherein, j represents the imaginary unit; S13, use the same method to set the bridge arm equivalent capacitor voltage v u , Submodule switching coefficient s u Converted to the frequency domain, the bridge arm current is obtained in phasor form , bridge arm equivalent capacitance voltage , Submodule switching coefficient : ； Among them, each element in the formula corresponds to the frequency from arrive The harmonic components of represents the fundamental frequency, Represents the equivalent capacitance voltage of the MMC bridge arm, Indicates the amplitude of the nth harmonic component of the submodule switching coefficient, Indicates the phase of the nth harmonic component of the MMC bridge arm current, Indicates the phase of the nth harmonic component of the equivalent capacitance voltage of the MMC bridge arm, Indicates the phase of the nth harmonic component of the submodule switching coefficient; S2, the bridge arm current in phase form , the bridge arm equivalent capacitance voltage , the submodule switching coefficient and the average value mathematical model of MMC in the time domain to obtain the steady-state frequency domain model of MMC; The step S2 specifically includes: S21, the bridge arm current of MMC , bridge arm equivalent capacitance voltage , Submodule switching coefficient Substituting the average value mathematical model in the MMC time domain into the frequency domain convolution operation instead of the product operation in the time domain, we can get: ； in, represents the DC voltage phasor, represents the voltage phasor on the AC side, is the DC side voltage of MMC, and are the voltage amplitude and phase angle of the MMC AC side, The admittance matrix representing the bridge arm reactance, The impedance matrix representing the equivalent capacitance of the bridge arm, is the equivalent resistance of the MMC bridge arm, is the equivalent reactance of the MMC bridge arm, is the equivalent capacitance of the MMC bridge arm; S22. Using the Toeplitz matrix, the phasor convolution operation is converted into a dot product operation between the matrix and the phasor, and the steady-state frequency domain model of the MMC is obtained: ； in, is the submodule switching factor The Toeplitz matrix form can be expressed as: ； in, represents the amplitude of the nth harmonic component of the submodule switching coefficient, j represents the imaginary unit, Indicates the phase of the nth harmonic component of the submodule switching coefficient; S3, according to the harmonic linearization method, the injection frequency at the common connection point of the steady-state frequency domain model is f s The voltage disturbance signal , and linearize the steady-state frequency domain model at the steady-state operating point to obtain a frequency domain small signal model of the MMC main circuit after the disturbance is injected; S4. Model each control link according to the MMC control system to obtain the small signal model of the submodule switching coefficient after the disturbance is injected. ; S5. Based on the frequency domain small signal model of the MMC main circuit and the small signal model of the submodule switching coefficient, solve the AC side impedance of the MMC .

2. A modular multilevel converter AC side impedance modeling method according to claim 1, characterized in that: The step S3 specifically includes: S31, the injection frequency at the common connection point is f s The voltage disturbance signal , the bridge arm current of the MMC after the disturbance is injected can be obtained , bridge arm equivalent capacitance voltage , Submodule switching coefficient : ； Among them, ^ represents the small signal variable corresponding to each variable; S32, inject the bridge arm current of the MMC after the disturbance , bridge arm equivalent capacitance voltage , Submodule switching coefficient Substitute it into the steady-state frequency domain model of MMC and linearize it at the steady-state operating point to obtain the frequency domain small signal model of the MMC main circuit after the disturbance is injected: ； in, , is the phase angle of the injected disturbance voltage signal, represents the admittance matrix of the bridge arm reactance after the disturbance is injected, The impedance matrix represents the equivalent capacitance of the bridge arm after the disturbance is injected, and They are the equivalent capacitance voltage of the MMC bridge arm , bridge arm current The Toeplitz matrix form can be expressed as: ； Where j represents the imaginary unit, is the amplitude of the nth harmonic component of the MMC bridge arm current, Represents the equivalent capacitance voltage of the MMC bridge arm, Indicates the phase of the nth harmonic component of the MMC bridge arm current, Indicates the phase of the nth harmonic component of the MMC bridge arm equivalent capacitor voltage.

3. A modular multilevel converter AC side impedance modeling method according to claim 2, characterized in that: The step S4 specifically includes: S41. Classify the internal harmonic phase sequence and phase of the MMC. The classification function is: Where k represents the harmonic order, and are classification functions of output components and circulation components, Indicates that this harmonic is the output component, Indicates that this harmonic is a circulating current component. Indicates that this harmonic is a circulating current component. Indicates that this harmonic is the output component, is the classification function of positive sequence component, negative sequence component and zero sequence component, Indicates that this harmonic is a positive sequence component, Indicates that this harmonic is a positive sequence component, Indicates that this harmonic is a zero-sequence component; S42, consider the current control inner loop to the MMC submodule switching coefficient The influence of the current control inner loop on the bridge arm current Control function for: ； in, represents the fundamental frequency, f s represents the frequency of the voltage disturbance signal, H i represents the current inner loop transfer function, K ip and K ii are the proportional coefficient and integral coefficient of the current inner loop PI controller respectively, j represents the imaginary unit, is the equivalent reactance of the MMC bridge arm; S43, considering the circulation suppression link to the MMC submodule switching coefficient The influence of circulating current suppression link on bridge arm current Control function for: ； in, H c represents the transfer function of the circulating current suppression link, K cirp and K ciri They are the proportional coefficient and integral coefficient of the PI controller in the circulating current suppression link respectively; S44, consider the DC voltage outer loop control link to the MMC sub-module switching coefficient The influence of DC voltage disturbance for: ； The DC voltage outer loop control link affects the DC voltage disturbance Control function for: ； in, is the equivalent impedance of the MMC DC side after the disturbance is injected, G dc represents the DC voltage outer loop control function, G ir represents the current inner loop forward path control function, H dc represents the DC voltage outer loop transfer function, K dcp and K dci are the proportional coefficient and integral coefficient of the DC voltage outer loop PI controller respectively; S45, considering the active power outer loop control link and the reactive power outer loop control link to the MMC submodule switching coefficient The influence of active power disturbance and reactive power disturbance They are: ； ； If the power outer loop control adopts active power control, the power outer loop control link will affect the active power disturbance Control function for: ； If the power outer loop control adopts reactive power control, the power outer loop control link will affect the reactive power disturbance Control function for: ； in, G P represents the active power outer loop control function, H P represents the active power outer loop transfer function, and are the proportional coefficient and integral coefficient of the active power outer loop PI controller respectively, G Q represents the reactive power outer loop control function, H Q represents the reactive power outer loop transfer function, and are the proportional coefficient and integral coefficient of the reactive power outer loop PI controller, Represents voltage disturbance signal; S46. For the MMC control system using DC voltage control and reactive power control, the small signal model of the submodule switching coefficient is obtained after injecting disturbance for: ； For the MMC control system using active power control and reactive power control, the small signal model of the submodule switching coefficient is obtained after injecting disturbance: for: ； in, To control link delay.

4. The method for modeling AC side impedance of a modular multilevel converter according to claim 1, characterized in that: The step S5 specifically includes: S51, small signal model of the switching coefficient of the submodule after the disturbance is injected Substitute into the frequency domain small signal model of the MMC main circuit to obtain the MMC AC side admittance : ； ； ； in, is the identity matrix, A i , A v , M i and M v are all intermediate variables. represents the bridge arm current of the MMC after the disturbance is injected, To control link delay, represents the voltage disturbance signal, represents the admittance matrix of the bridge arm reactance after the disturbance is injected, The impedance matrix represents the equivalent capacitance of the bridge arm after the disturbance is injected, and They are the equivalent capacitance voltage of the MMC bridge arm , bridge arm current The Toeplitz matrix form of is the submodule switching factor The Toeplitz matrix form of ; S52, according to the AC side admittance Calculate the AC side impedance : 。 5. A modular multilevel converter AC side impedance modeling terminal, comprising a processor, a memory, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the steps in any one of the modular multilevel converter AC side impedance modeling methods of claims 1-4 are implemented.

Images