Impedance modeling and analysis method of back-to-back flexible DC system considering AC / DC coupling

Abstract

The present invention provides a back-to-back flexible DC system impedance modeling and analysis method considering AC / DC coupling, and the modeling method includes the following steps: S1: establishing a small signal impedance model of a single-ended open-loop MMC converter station; S2: analyzing the influence of double closed-loop control on the small signal impedance model on the rectifier side and the inverter side, and obtaining a double closed-loop control small signal impedance model; S3: obtaining the steady-state parameters required for the small signal impedance modeling of the MMC converter station; solving the AC impedance curve and DC impedance curve of the MMC converter station on the rectifier side, and the AC impedance curve and DC impedance curve of the MMC converter station on the inverter side; S4, analyzing the harmonic transfer relationship between the MMC converter stations on the rectifier side and the inverter side, eliminating the coupling of the AC grid impedance to the system, and combining the double closed-loop control small signal impedance models on the rectifier side and the inverter side. The impedance model established by the modeling method of the present invention can be used to accurately analyze the stability of the impedance between two MMC converter stations and between the back-to-back flexible DC system and the grid.

Description

Technical Field

[0001] The present invention belongs to the technical field of impedance modeling of direct current transmission and distribution, and in particular relates to an impedance modeling and analysis method for a back-to-back flexible direct current system considering alternating current and direct current coupling. Background Art

[0002] With the proposal of the "dual carbon" goals, the country vigorously advocates the development of new energy represented by wind energy. In order to improve the efficiency of energy transmission, flexible direct current transmission projects have gradually become popular in the process of new energy transmission.

[0003] The significant feature of flexible DC transmission is the use of modular multilevel converter (MMC), which has the advantages of high transmission efficiency, good output waveform quality, and strong scalability. However, MMC has internal circulating currents, harmonics in capacitor voltages, and inherent nonlinear characteristics in the control system, which makes its dynamic characteristics complex and easy to interact with the interconnected power grid, causing harmonic oscillations, and then serious safety accidents; subsynchronous oscillations, supersynchronous oscillations, and high-frequency oscillations have occurred many times in existing back-to-back flexible DC projects. The back-to-back flexible DC system includes a rectifier side and an inverter side converter station. The rectifier side is connected to a low short-circuit ratio power grid, and the inverter side is connected to a strong power grid; the bridge arm parameters of the MMC in the converter stations on both sides are the same, where the rectifier side uses DC voltage plus reactive power control, and the inverter side uses active power plus reactive power control to ensure the stability of the back-to-back flexible DC system.

[0004] Therefore, in order to ensure the stability of the back-to-back flexible DC system, an accurate and concise stability analysis method is needed. The traditional time domain analysis method requires complex formula derivation, and as the number of modules increases, the calculation difficulty increases exponentially and is not easy to verify in actual projects; the frequency domain analysis method represented by the impedance analysis method has a simple analysis process, and can accurately judge and predict the stability of the back-to-back flexible DC system with the Nyquist criterion, and the impedance has practical significance, which is convenient for measurement and verification in actual projects. The impedance analysis method can be divided into two analysis methods: based on harmonic state space and multi-harmonic linearization. The two are equivalent, but the harmonic state space derivation is slightly simpler and easier to program.

[0005] However, the impedance modeling in the field of power transmission and distribution is currently mostly based on a single converter station, without considering the harmonic transmission and impedance coupling between multi-terminal converter stations. It is impossible to accurately model the impedance of the back-to-back MMC system using only the single-ended MMC equivalent model. There are limitations in its use, which may lead to misjudgment of stability.

[0006] In summary, when modeling the impedance of the double-terminal MMC in the back-to-back flexible DC system, how to accurately analyze the stability of the impedance between the two MMC converter stations and between the back-to-back flexible DC system and the power grid has become a problem that needs to be solved urgently. Summary of the invention

[0007] In view of the above-mentioned deficiencies in the prior art, the present invention provides a back-to-back flexible DC system impedance modeling method considering AC / DC coupling. The established impedance model can be used to accurately analyze the stability of the impedance between two MMC converter stations and between the back-to-back flexible DC system and the power grid.

[0008] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0009] The impedance modeling method of the back-to-back flexible DC system considering AC / DC coupling is proposed. The back-to-back flexible DC system includes rectifier and inverter side converter stations. The rectifier side is connected to a power grid with a low short-circuit ratio, and the inverter side is connected to a strong power grid. The bridge arm parameters of the MMC in the converter stations on both sides are the same. The rectifier side adopts DC voltage plus reactive power control, and the inverter side adopts active power plus reactive power control. The impedance modeling method includes the following steps:

[0010] S1: Using the harmonic state space method, a small signal impedance model of a single-ended open-loop MMC converter station is established;

[0011] S2: Based on the small signal impedance model of the single-ended open-loop MMC converter station, combined with the control methods of the rectifier and inverter-side MMC converter stations, the influence of the dual closed-loop control of the rectifier and inverter-side MMC converter stations on the small signal impedance model is analyzed, and the dual closed-loop control small signal impedance model of the MMC converter station is obtained;

[0012] S3: Obtain the steady-state parameters required for small-signal impedance modeling of the MMC converter station by means of online simulation monitoring; Combined with the dual closed-loop control small-signal impedance model obtained in step 2, respectively solve the AC impedance curve and DC impedance curve of the MMC converter station on the rectifier side, and the AC impedance curve and DC impedance curve of the MMC converter station on the inverter side;

[0013] S4, according to the impedance curve obtained in S3, analyze the harmonic transfer relationship between the MMC converter stations on the rectifier side and the inverter side, eliminate the coupling of the AC grid impedance to the system, combine the dual closed-loop control small signal impedance models of the rectifier side and the inverter side, and obtain the impedance model of the back-to-back flexible DC system; and draw the analytical impedance curve under closed-loop control of the back-to-back flexible DC system.

[0014] Preferably, S1 includes:

[0015] S11, using the average model to model the MMC converter station, and obtaining the time domain differential common mode circuit equations of the MMC converter station through the mathematical transformation form of differential common mode decomposition;

[0016] S12, by introducing small signal analysis and Fourier series expansion theory, the time domain difference common mode circuit equation of the MMC converter station obtained in S11 is converted into a frequency domain small signal equation;

[0017] S13. Using the principle of harmonic balance, the time-varying terms and transient variables of the frequency domain small signal equation obtained in S12 are eliminated to obtain the harmonic state equation of the MMC converter station for the nth harmonic, and the Toeplitz matrix is ​​used to write the harmonic state equation in the form of a steady-state matrix as the harmonic state space matrix that characterizes the frequency information of the MMC converter station; then only focusing on the open-loop external characteristics of the MMC converter station, ignoring the control link, the disturbance voltage and current are compared to obtain the small signal impedance model of the single-ended open-loop MMC converter station.

[0018] Preferably, in S11, the time domain difference common mode circuit equation is:

[0019]

[0020] In the formula, the superscripts ± and 0 represent the positive sequence and negative sequence parameters, respectively; u gdc is the equivalent DC voltage of the converter station, u gac is the equivalent AC voltage of the converter station, u dm and u cm They are the bridge arm differential common mode voltage, i cm is the common mode current of the bridge arm, R is the bridge arm resistance, L is the bridge arm inductance, C is the submodule capacitance, i ac Indicates the MMC AC side current, m dm and m cm Respectively represent the MMC differential common mode modulation function, u Cdm is the capacitance difference, u Ccm is the common mode voltage, Z gdc is the DC impedance connected to the single-ended MMC, Z gac is the connected AC impedance.

[0021] Preferably, in S12, the small signal expansion process is as follows:

[0022]

[0023] The process of substituting the Fourier series of the first term on the right side of the time domain small signal equation includes:

[0024]

[0025] In the formula, x(t) represents the state quantity, a(t) and b(t) represent the system parameters or control parameters, u(t) represents the input quantity, the subscript and superscript n or m represent the harmonic order, the subscript p represents the injection disturbance frequency, and ω 1 is the common frequency, j is the imaginary unit, j(p+n) represents the p+n harmonic generated after the disturbance is coupled inside the MMC, j(nm) represents the nm harmonic, and j(p+m) represents the p+m harmonic.

[0026] Preferably, in S13, the harmonic state equation of the MMC converter station for the nth harmonic is:

[0027]

[0028] The harmonic state equation is written in the form of a steady-state matrix using the Toeplitz matrix as the harmonic state space matrix:

[0029]

[0030] In the harmonic state space matrix, the subscript of the matrix parameter represents the parameter frequency information.

[0031] Preferably, in S13, the harmonic state space matrix characterizing the frequency information of the MMC converter station is:

[0032]

[0033]

[0034]

[0035] And in S13, Δm dm , Δm cm Set to an all-zero matrix;

[0036] Where E represents the order parameter screening matrix, for example, E 0 represents the zero-sequence screening matrix, E ± represents the positive and negative sequence screening matrix, I represents the unit matrix, S represents the perturbation coefficient matrix, and N represents the number of MMC sub-modules.

[0037] Preferably, in S2, after analyzing the influence of the double closed-loop control of the MMC converter station on the rectifier side and the inverter side on the small signal impedance model, Δm dm , Δm cm Added as follows:

[0038]

[0039] Among them, G i11 Represents the circulation controller G icm For Δm cmThe disturbance effect of G i22 G is the inner current loop controller i For Δm dm The impact of G u21 G is the DC voltage outer loop controller udc For Δm dm The impact of G u22 G is the phase-locked loop controller pll For Δm dm The impact of G' u22 G is the outer loop active power control pq And the phase-locked loop controller G' under power control pll The impact of dc Indicates the equivalent DC voltage of a single MMC, u ac is the AC voltage of a single MMC;

[0040]

[0041] Among them, T d+ represents park transformation, T d- represents the inverse Park transform, u d+ 、u q+ 、i' d +、i' q+ 、m' d+ 、m' q+ 、m d+ 、m q+ Indicates the additional impact caused by park transformation and phase-locked loop, T q+ and T q- Respectively represent the positive and negative park transformation of the q axis, i d and i q They represent the d-axis and q-axis components of the MMC AC output current, respectively. d and u q They represent the d-axis and q-axis components of the grid voltage respectively.

[0042] Preferably, in S3, the DC equivalent voltage u is considered gdc With MMC control voltage u dc The relationship Δu dc =Δu gdc -Δi dc Z gdc , substituted into the S2 closed-loop equation to obtain the AC and DC impedance expressions, and the steady-state parameters required for the small signal impedance modeling of the MMC converter station are obtained by using the simulation online monitoring method, and the AC impedance Z of the MMC converter station is obtained. MMC_ac , DC impedance Z MMC_dc The specific expression of:

[0043]

[0044] In the formula, I 7 is the 7th-order unit matrix, 0 represents the 7th-order all-zero matrix, Z gdc is the DC impedance connected to the single-ended MMC, Z gac is the connected AC impedance; K mdm1 is the control coefficient matrix 1, K mdm2 is the control coefficient matrix 2; where, if the DC side impedance is required, Δu gac Set to zero and calculate the AC impedance. gdc Set to zero.

[0045] Preferably, in S4, the process of drawing an analytical impedance curve under closed-loop control of the back-to-back flexible DC system includes:

[0046] First, the harmonic transfer relationship of the single-ended MMC converter station under AC disturbance injection is analyzed, and the AC analytical impedance of the single-ended MMC converter station is obtained:

[0047]

[0048] Among them, ω p is the voltage disturbance injected into the AC end; pcc is the intersection of the rectifier side and the grid impedance; Z aco (ω p ) is the AC side impedance of the MMC converter station including the grid impedance;

[0049] Secondly, the influence of the inverter side impedance when converting the single-ended MMC converter station into a back-to-back flexible DC system is analyzed, and the fixed DC impedance Z in the corresponding harmonic state space matrix is ​​converted into gdc Replaced by a frequency-dependent dynamic impedance Z MMC2 (ω p -ω 1 ):

[0050]

[0051] Among them, (ω p -ω 1 ) is ω p The voltage disturbance ω injected into the AC terminal p The harmonic order of the DC side when u dc Single MMC DC voltage, i dc Corresponding DC current of MMC;

[0052] Finally, the impedance modeling process of the inverter-side MMC converter station in S1-S3 is used to provide a disturbance voltage with a wide frequency range to obtain Z MMC2 (ω p -ω 1 ), and then the analytical impedance curve of the back-to-back flexible DC system considering the coupling relationship between the AC and DC sides is obtained.

[0053] In addition, the present invention also provides an impedance analysis method for a back-to-back flexible DC system considering AC / DC coupling. The above method is used to establish an impedance model of the back-to-back flexible DC system. The impedance model is used to calculate the impedance between the two MMC converter stations in the back-to-back flexible DC system and the impedance between the back-to-back flexible DC system and the power grid. Then, based on the impedance measurement results, the stability of the impedance between the two MMC converter stations in the back-to-back flexible DC system and the impedance between the back-to-back flexible DC system and the power grid is analyzed.

[0054] Compared with the prior art, the present invention has the following beneficial effects:

[0055] 1. Compared with the prior art, the modeling method of the present invention takes into account many controllers of the MMC converter station in the process of modeling the impedance of the back-to-back flexible DC system, and considers the mirror coupling relationship of the impedance between the back-to-back flexible DC system and the power grid in the modeling process, so that the modeling result is more accurate. In addition, the present invention fully considers the harmonic transfer relationship between the two converter stations in the back-to-back flexible DC system, establishes an accurate two-terminal equivalent impedance, and has higher accuracy than the single MMC converter station model. It solves the problem of low accuracy of the impedance modeling of the existing back-to-back flexible DC system, and has high practical value for analyzing the stability of the system power grid interconnection. Through simulation verification, it is found that the model established by the modeling method of the present invention is used to measure the impedance between the two MMC converter stations in the back-to-back flexible DC system and the impedance between the back-to-back flexible DC system and the power grid, which can be highly consistent with the simulation results. Therefore, it can be used to accurately analyze the stability of the impedance between the two MMC converter stations and between the back-to-back flexible DC system and the power grid.

[0056] 2. The modeling method of the present invention takes into account many controllers of the MMC converter station in the process of modeling the impedance of the back-to-back flexible DC system, and has high scalability.

[0057] 3. The operation of the modeling method of the present invention is relatively simple and easy, and in the specific process of modeling and analysis, the steady-state parameters of simulation monitoring are used, which not only ensures the clarity of the principle but also ensures the reliability of the results. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] In order to make the purpose, technical solution and advantages of the invention more clear, the present invention will be further described in detail below with reference to the accompanying drawings, in which:

[0059] Figure 1 A topological structure diagram of a back-to-back flexible DC system in an embodiment;

[0060] Figure 2 is a flow chart of an embodiment;

[0061] Figure 3 It is a diagram of various control strategies of MMC in the embodiment;

[0062] Figure 4 Schematic diagram of harmonic transfer of a back-to-back flexible DC system in an embodiment;

[0063] Figure 5 This is a comparison diagram of the inverter-side MMC DC side analytical impedance and the frequency sweep result in the embodiment;

[0064] Figure 6 This is a comparison diagram of the analytical impedance and frequency sweep results of the back-to-back flexible DC system in the embodiment. DETAILED DESCRIPTION

[0065] The following is a further detailed description through specific implementation methods:

[0066] Example:

[0067] This embodiment discloses an impedance modeling method for a back-to-back flexible DC system considering AC / DC coupling.

[0068] The back-to-back flexible DC system includes rectifier and inverter side converter stations. The rectifier side is connected to a low short-circuit ratio grid, and the inverter side is connected to a strong grid. The specific topology diagram is as follows: Figure 1 As described above, the bridge arm parameters of the MMC in the converter stations on both sides are the same, wherein the rectifier side adopts DC voltage plus reactive power control, and the inverter side adopts active power plus reactive power control to ensure the stability of the back-to-back flexible DC system.

[0069] like Figure 2 As shown, the impedance modeling method includes the following steps:

[0070] S1: Using the harmonic state space method, a small signal impedance model of the single-ended open-loop MMC converter station is established.

[0071] In specific implementation, S1 includes:

[0072] S11. The MMC converter station is modeled using the average model, and the time domain differential common mode circuit equations of the MMC converter station are obtained through the mathematical transformation form of differential common mode decomposition.

[0073] Among them, the time domain difference common mode circuit equation is:

[0074]

[0075] In the formula, the superscripts ± and 0 represent the positive sequence and negative sequence parameters, respectively; u gdc is the equivalent DC voltage of the converter station, u gac is the equivalent AC voltage of the converter station, u dm and u cmare the bridge arm differential common mode voltage, i cm is the common mode current of the bridge arm, R is the bridge arm resistance, L is the bridge arm inductance, C is the submodule capacitance, i ac Indicates the MMC AC side current, m dm and m cm Respectively represent the MMC differential common mode modulation function, u Cdm is the capacitance difference, u Ccm is the common mode voltage, Z gdc is the DC impedance connected to the single-ended MMC, Z gac is the connected AC impedance.

[0076] S12. By introducing small signal analysis and Fourier series expansion theory, the time domain difference common mode circuit equation of the MMC converter station obtained in S11 is converted into a frequency domain small signal equation.

[0077] Among them, the small signal expansion process is as follows:

[0078]

[0079] The process of substituting the Fourier series of the first term on the right side of the time domain small signal equation includes:

[0080]

[0081] In the formula, x(t) represents the state quantity, a(t) and b(t) represent the system parameters or control parameters, u(t) represents the input quantity, the subscript and superscript n or m represent the harmonic order, the subscript p represents the injection disturbance frequency, and ω 1 is the common frequency, j is the imaginary unit, j(p+n) represents the p+n harmonic generated after the disturbance is coupled inside the MMC, j(nm) represents the nm harmonic, and j(p+m) represents the p+m harmonic.

[0082] S13. Using the principle of harmonic balance, the time-varying terms and transient variables of the frequency domain small signal equation obtained in S12 are eliminated to obtain the harmonic state equation of the MMC converter station for the nth harmonic, and the Toeplitz matrix is ​​used to write the harmonic state equation in the form of a steady-state matrix as the harmonic state space matrix that characterizes the frequency information of the MMC converter station; then only focusing on the open-loop external characteristics of the MMC converter station, ignoring the control link, the disturbance voltage and current are compared to obtain the small signal impedance model of the single-ended open-loop MMC converter station.

[0083] The harmonic state equation of the MMC converter station for the nth harmonic is:

[0084]

[0085] The harmonic state equation is written in the form of a steady-state matrix using the Toeplitz matrix as the harmonic state space matrix:

[0086]

[0087] In the harmonic state space matrix, the subscript of the matrix parameter represents the parameter frequency information.

[0088] The harmonic state space matrix representing the frequency information of the MMC converter station is:

[0089]

[0090]

[0091]

[0092] And in S13, Δm dm , Δm cm Set to an all-zero matrix;

[0093] E represents the order parameter screening matrix, for example, E 0 represents the zero-sequence screening matrix, E ± represents the positive and negative sequence screening matrix, I represents the unit matrix, S represents the perturbation coefficient matrix, and N represents the number of MMC sub-modules.

[0094] S2: Based on the small signal impedance model of the single-ended open-loop MMC converter station, the control methods of the rectifier and inverter side MMC converter stations are combined, such as Figure 3 As shown, the influence of the dual closed-loop control of the MMC converter station on the rectifier side and the inverter side on the small signal impedance model is analyzed, and the dual closed-loop control small signal impedance model of the MMC converter station is obtained.

[0095] In the specific implementation, after analyzing the influence of the double closed-loop control of the MMC converter station on the rectifier side and the inverter side on the small signal impedance model, Δm dm , Δm cm Added as follows:

[0096]

[0097] Among them, G i11 Represents the circulation controller G icm For Δm cm The disturbance effect of G i22 G is the inner current loop controller i For Δm dm The impact of G u21 G is the DC voltage outer loop controller udc For Δm dm The impact of G u22 G is the phase-locked loop controllerpll For Δm dm The influence of G'u22 is the outer loop active power control G pq And the phase-locked loop controller G' under power control pll The impact of dc Indicates the equivalent DC voltage of a single MMC, u ac is the AC voltage of a single MMC;

[0098]

[0099] Among them, T d+ represents park transformation, T d- represents the inverse Park transform, u d+ 、u q+ 、i' d+ 、i' q+ 、m' d+ 、m' q+ 、m d+ 、m q+ Indicates the additional impact caused by park transformation and phase-locked loop, T q+ and T q- Respectively represent the positive and negative park transformation of the q axis, i d and i q They represent the d-axis and q-axis components of the MMC AC output current, respectively. d and u q They represent the d-axis and q-axis components of the grid voltage respectively.

[0100] S3: Consider the DC equivalent voltage u gdc With MMC control voltage u dc The relationship Δu dc =Δu gdc -Δi dc Z gdc , by substituting it into the S2 closed-loop equation, the AC and DC impedance expressions can be obtained. By simulating online monitoring, the steady-state parameters required for small-signal impedance modeling of the MMC converter station can be obtained. Combined with the dual closed-loop control small-signal impedance model obtained in step 2, the AC impedance curve and DC impedance curve of the MMC converter station on the rectifier side, as well as the AC impedance curve and DC impedance curve of the MMC converter station on the inverter side are solved respectively.

[0101] In the specific implementation, the steady-state parameters required for the small signal impedance modeling of the MMC converter station are obtained by using the simulation online monitoring method, and the AC impedance Z of the MMC converter station is obtained. MMC_ac , DC impedance Z MMC_dc The specific expression of:

[0102]

[0103] In the formula, I7 is the 7th-order unit matrix, 0 represents the 7th-order all-zero matrix, Z gdc is the DC impedance connected to the single-ended MMC, Z gac is the connected AC impedance; K mdm1 is the control coefficient matrix 1, K mdm2 is the control coefficient matrix 2; if the DC side impedance is required, Δu gac Set to zero and calculate the AC impedance. gdc Set to zero.

[0104] S4, according to the impedance curve obtained in S3, analyze the harmonic transfer relationship between the MMC converter stations on the rectifier side and the inverter side, eliminate the coupling of the AC grid impedance to the system, combine the dual closed-loop control small signal impedance models of the rectifier side and the inverter side, and obtain the impedance model of the back-to-back flexible DC system; and draw the analytical impedance curve under closed-loop control of the back-to-back flexible DC system.

[0105] In specific implementation, the process of drawing the analytical impedance curve under the closed-loop control of the back-to-back flexible DC system includes:

[0106] First, the harmonic transfer relationship of the single-ended MMC converter station under AC disturbance injection is analyzed, and the AC analytical impedance of the single-ended MMC converter station is obtained:

[0107]

[0108] Among them, ω p is the voltage disturbance injected into the AC end; pcc is the intersection of the rectifier side and the grid impedance; Z aco (ω p ) is the AC side impedance of the MMC converter station including the grid impedance;

[0109] Secondly, the influence of inverter side impedance when converting the single-ended MMC converter station into a back-to-back flexible DC system is analyzed.

[0110] When the object is converted into a back-to-back flexible DC system, the harmonic transfer relationship is as follows: Figure 4 As shown. The fixed DC impedance Z in the corresponding harmonic state space matrix gdc Replaced by a frequency-dependent dynamic impedance Z MMC2 (ω p -ω 1 ):

[0111]

[0112] Among them, (ω p -ω 1 ) is ω p The voltage disturbance ω injected into the AC terminal p The harmonic order of the DC side when udc Single MMC DC voltage, i dc Corresponding DC current of MMC;

[0113] Finally, the impedance modeling process of the inverter-side MMC converter station in S1-S3 is used to provide a disturbance voltage with a wide frequency range to obtain Z MMC2 (ω p -ω 1 ), where the analysis and frequency sweep results are as follows Figure 5 As shown, the analytical impedance curve of the back-to-back flexible DC system considering the coupling relationship between the AC and DC sides is obtained.

[0114] To verify the effectiveness of the modeling method of the present invention, a broadband disturbance can be injected into the AC bus of the simulation system to obtain the precise impedance sweep characteristic points of the back-to-back flexible DC system within a certain frequency range; then the sweep characteristic points are analyzed for consistency with the established analytical impedance curve to verify the correctness of the proposed modeling method.

[0115] Specifically, the parameters of the main circuit and control circuit of the back-to-back flexible DC system are kept unchanged during the solution of the analytical impedance curve. Considering the degree of data visualization, 100Hz is used as the demarcation point, and the disturbance voltage is injected every 2Hz within 100Hz. The measurement interval above 100Hz is changed to 20Hz, and the corresponding impedance is measured, and finally the precise impedance sweep feature points of the back-to-back flexible DC system within the wide-band disturbance range are obtained. The measured sweep feature points are analyzed for consistency with the analytical impedance curve established by the modeling method of the present invention, and the consistency reference coefficient is set to α. It is believed that if α is within the ±5% trust band, the data of the analytical impedance curve at this point is valid. The correctness of the proposed modeling method is verified by multi-point simultaneous consistency analysis, where the specific expression of α is:

[0116]

[0117] In the formula, Z th It represents the analytical impedance value of the back-to-back flexible DC system established by this patent at the characteristic frequency, Z me The inventors have obtained a comparison chart of the analytical impedance and the frequency sweep result of the back-to-back flexible DC system through specific implementation, as shown in the figure. Figure 6 As shown, through Figure 6From the comparison between the analytical impedance and the frequency sweep results, it can be seen that all characteristic points are near the analytical impedance curve, satisfying the 5% trust band. The method proposed in this patent can be used to carry out stability analysis of the back-to-back flexible DC system. Through simulation verification, it is found that the impedance between the two MMC converter stations in the back-to-back flexible DC system and the impedance between the back-to-back flexible DC system and the power grid are calculated using the model established by the modeling method of the present invention, which is highly consistent with the simulation results. Therefore, it can be used to accurately analyze the stability of the impedance between the two MMC converter stations and between the back-to-back flexible DC system and the power grid.

[0118] Compared with the prior art, the modeling method of the present invention takes into account many controllers of the MMC converter station in the process of modeling the impedance of the back-to-back flexible DC system, and considers the mirror coupling relationship of the impedance between the back-to-back flexible DC system and the power grid during the modeling process, so that the modeling result is more accurate. In addition, the present invention fully considers the harmonic transfer relationship between the two converter stations in the back-to-back flexible DC system, establishes an accurate two-terminal equivalent impedance, and has higher accuracy than the single MMC converter station model. It solves the problem of low accuracy of the impedance modeling of the existing back-to-back flexible DC system, and has high practical value for analyzing the stability of the system power grid interconnection. Through simulation verification, it is found that the model established by the modeling method of the present invention is used to measure the impedance between the two MMC converter stations in the back-to-back flexible DC system and the impedance between the back-to-back flexible DC system and the power grid, which can be highly consistent with the simulation results, so it can be used to accurately analyze the stability of the impedance between the two MMC converter stations and between the back-to-back flexible DC system and the power grid. In addition, the modeling method of the present invention takes into account many controllers of the MMC converter station in the process of modeling the impedance of the back-to-back flexible DC system, and has high scalability. In addition, the operation of the modeling method of the present invention is relatively simple and easy, and in the specific process of modeling and analysis, the steady-state parameters of simulation monitoring are used, which not only ensures the clear principle but also ensures the reliability of the results.

[0119] The present invention also provides an impedance analysis method for a back-to-back flexible DC system considering AC / DC coupling. The above method is used to establish an impedance model of the back-to-back flexible DC system. The impedance model is used to calculate the impedance between the two MMC converter stations in the back-to-back flexible DC system and the impedance between the back-to-back flexible DC system and the power grid. Then, according to the impedance measurement results, the stability of the impedance between the two MMC converter stations in the back-to-back flexible DC system and the impedance between the back-to-back flexible DC system and the power grid is analyzed.

[0120] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit the technical solution. Those skilled in the art should understand that those modifications or equivalent substitutions of the technical solution of the present invention that do not depart from the purpose and scope of the technical solution should be included in the scope of the claims of the present invention.

Claims

1. Impedance modeling method of back-to-back flexible DC system considering AC / DC coupling, Features: The back-to-back flexible DC system includes rectifier and inverter side converter stations. The rectifier side is connected to a low short-circuit ratio power grid, and the inverter side is connected to a strong power grid. The bridge arm parameters of the MMCs in the converter stations on both sides are the same. The rectifier side adopts DC voltage plus reactive power control, and the inverter side adopts active power plus reactive power control. The impedance modeling method includes the following steps: S1: Using the harmonic state space method, a small signal impedance model of a single-ended open-loop MMC converter station is established; S2: Based on the small signal impedance model of the single-ended open-loop MMC converter station, combined with the control methods of the rectifier and inverter-side MMC converter stations, the influence of the dual closed-loop control of the rectifier and inverter-side MMC converter stations on the small signal impedance model is analyzed, and the dual closed-loop control small signal impedance model of the MMC converter station is obtained; in, After analyzing the influence of the double closed-loop control of the MMC converter station on the rectifier and inverter sides on the small signal impedance model, the Δm dm , Δm cm Added as follows: Among them, G i11 Represents the circulation controller G icm For Δm cm The disturbance effect of G i22 G is the inner current loop controller i For Δm dm The impact of G u21 G is the DC voltage outer loop controller udc For Δm dm The impact of G u22 G is the phase-locked loop controller pll For Δm dm The influence of G′ u22 G is the outer loop active power control pq And the phase-locked loop controller G′ under power control pll The impact of dc Indicates the equivalent DC voltage of a single MMC, u ac is the AC voltage of a single MMC; m dm and m cm Respectively represent the MMC differential and common mode modulation functions; T d+ and T d- Respectively represent the positive and negative Park transformation of the d-axis, and u d+ 、u q+ , i′ d+ , i′ q+ , m′ d+ , m′ q+ 、m d+ 、m q+ Indicates the additional impact caused by park transformation and phase-locked loop, T q+ and T q- Respectively represent the positive and negative park transformation of the q axis, i d and i q They represent the d-axis and q-axis components of the MMC AC output current, respectively. d and u q Then they represent the d-axis and q-axis components of the grid voltage respectively; S3: Obtain the steady-state parameters required for small-signal impedance modeling of the MMC converter station by means of online simulation monitoring; Combined with the dual closed-loop control small-signal impedance model obtained in step 2, respectively solve the AC impedance curve and DC impedance curve of the MMC converter station on the rectifier side, and the AC impedance curve and DC impedance curve of the MMC converter station on the inverter side; S4, according to the impedance curve obtained in S3, analyze the harmonic transfer relationship between the MMC converter stations on the rectifier side and the inverter side, eliminate the coupling of the AC grid impedance to the system, combine the dual closed-loop control small signal impedance models of the rectifier side and the inverter side, and obtain the impedance model of the back-to-back flexible DC system; and draw the analytical impedance curve under closed-loop control of the back-to-back flexible DC system.

2. The impedance modeling method of a back-to-back flexible DC system considering AC / DC coupling as claimed in claim 1, Features: S1 includes: S11, using the average model to model the MMC converter station, and obtaining the time domain differential common mode circuit equations of the MMC converter station through the mathematical transformation form of differential common mode decomposition; S12, by introducing small signal analysis and Fourier series expansion theory, the time domain difference common mode circuit equation of the MMC converter station obtained in S11 is converted into a frequency domain small signal equation; S13. Using the principle of harmonic balance, the time-varying terms and transient variables of the frequency domain small signal equation obtained in S12 are eliminated to obtain the harmonic state equation of the MMC converter station for the nth harmonic, and the Toeplitz matrix is ​​used to write the harmonic state equation in the form of a steady-state matrix as the harmonic state space matrix that characterizes the frequency information of the MMC converter station; then only focusing on the open-loop external characteristics of the MMC converter station, ignoring the control link, the disturbance voltage and current are compared to obtain the small signal impedance model of the single-ended open-loop MMC converter station.

3. The impedance modeling method of a back-to-back flexible DC system considering AC / DC coupling as claimed in claim 2, Features: In S11, the time domain difference common mode circuit equation is: In the formula, the superscripts ± and 0 represent the positive sequence and negative sequence parameters, respectively; u gdc is the equivalent DC voltage of the converter station, u gac is the equivalent AC voltage of the converter station, u dm and u cm are the bridge arm differential common mode voltage, i cm is the common mode current of the bridge arm, R is the bridge arm resistance, L is the bridge arm inductance, C is the submodule capacitance, i ac Indicates the MMC AC side current, m dm and m cm Respectively represent the MMC differential common mode modulation function, u Cdm is the capacitance difference, u Ccm is the common mode voltage, Z gdc is the DC impedance connected to the single-ended MMC, Z gac is the connected AC impedance.

4. The impedance modeling method of a back-to-back flexible DC system considering AC / DC coupling as claimed in claim 3, Features: In S12, the small signal expansion process is as follows: The process of substituting the Fourier series of the first term on the right side of the time domain small signal equation includes: In the formula, x(t) represents the state quantity, a(t) and b(t) represent the system parameters or control parameters, u(t) represents the input quantity, the subscript and superscript n or m represent the harmonic order, the subscript p represents the injection disturbance frequency, and ω 1 is the common frequency, j is the imaginary unit, j(p+n) represents the p+n harmonic generated after the disturbance is coupled inside the MMC, j(nm) represents the nm harmonic, and j(p+m) represents the p+m harmonic.

5. The impedance modeling method of a back-to-back flexible DC system considering AC / DC coupling as claimed in claim 4, Features: In S13, the harmonic state equation of the MMC converter station for the nth harmonic is: The harmonic state equation is written in the form of a steady-state matrix using the Toeplitz matrix as the harmonic state space matrix: In the harmonic state space matrix, the subscript of the matrix parameter represents the parameter frequency information.

6. The impedance modeling method of a back-to-back flexible DC system considering AC / DC coupling as claimed in claim 5, Features: In S13, the harmonic state space matrix representing the frequency information of the MMC converter station is: And in S13, Δm dm , Δm cm Set to an all-zero matrix; Among them, E represents the order parameter screening matrix, E 0 represents the zero-sequence screening matrix, E ± represents the positive and negative sequence screening matrix, I represents the unit matrix, S represents the perturbation coefficient matrix, and N represents the number of MMC sub-modules.

7. The impedance modeling method of a back-to-back flexible DC system considering AC / DC coupling as claimed in claim 6, Features: In S3, consider the DC equivalent voltage u gdc With MMC control voltage u dc The relationship Δu dc =Δu gdc -Δi dc Z gdc , substituted into the S2 closed-loop equation, the AC and DC impedance expressions can be obtained, and the steady-state parameters required for the small signal impedance modeling of the MMC converter station can be obtained by using the simulation online monitoring method, and the AC impedance Z of the MMC converter station can be obtained. MMC_ac , DC impedance Z MMC_dc The specific expression of: In the formula, I 7 is the 7th-order unit matrix, 0 represents the 7th-order all-zero matrix, Z gdc is the DC impedance connected to the single-ended MMC, Z gac is the connected AC impedance; if the DC side impedance is required, Δu gac Set to zero and calculate the AC impedance. gdc Set to zero.

8. The impedance modeling method of a back-to-back flexible DC system considering AC / DC coupling as claimed in claim 7, Features: In S4, the process of drawing the analytical impedance curve under the closed-loop control of the back-to-back flexible DC system includes: First, the harmonic transfer relationship of the single-ended MMC converter station under AC disturbance injection is analyzed, and the AC analytical impedance of the single-ended MMC converter station is obtained: Among them, ω p is the voltage disturbance injected into the AC end; pcc is the intersection of the rectifier side and the grid impedance; Z aco (ω p ) is the AC side impedance of the MMC converter station including the grid impedance; Secondly, the influence of the inverter side impedance when converting the single-ended MMC converter station into a back-to-back flexible DC system is analyzed, and the fixed DC impedance Z in the corresponding harmonic state space matrix is ​​converted into gdc Replaced by a frequency-dependent dynamic impedance Z MMC2 (ω p -ω 1 ): Among them, (ω p -ω 1 ) is ω p The voltage disturbance ω injected into the AC terminal p The harmonic order of the DC side when u dc Single MMC DC voltage, i dc Corresponding DC current of MMC; Finally, the impedance modeling process of the inverter-side MMC converter station in S1-S3 is used to provide a disturbance voltage with a wide frequency range to obtain Z MMC2 (ω p -ω 1 ), and then the analytical impedance curve of the back-to-back flexible DC system considering the coupling relationship between the AC and DC sides is obtained.

9. Impedance analysis method of back-to-back flexible DC system considering AC / DC coupling, Features: An impedance model of a back-to-back flexible DC system is established by the method described in any one of claims 1 to 8, and the impedance model is used to calculate the impedance between the two MMC converter stations in the back-to-back flexible DC system and the impedance between the back-to-back flexible DC system and the power grid, and then the stability of the impedance between the two MMC converter stations in the back-to-back flexible DC system and the impedance between the back-to-back flexible DC system and the power grid is analyzed based on the impedance measurement results.

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