Online Calculation Method and Device for Wideband Impedance of Modular Multilevel DC Transformer

Abstract

The present application discloses a method and device for online calculation of broadband impedance of a modular multilevel DC transformer, which relates to the field of DC transformers. The method includes: obtaining the relationships of various electrical quantities during the steady-state operation of the modular multilevel DC transformer based on the circuit topology of the modular multilevel DC transformer; establishing a power circuit model based on the relationships of various electrical quantities during the steady-state operation; establishing a control circuit model based on the input and output of the controller group of the modular multilevel DC transformer; establishing a small-signal impedance model based on the power circuit model and the control circuit model; and calculating the broadband impedance of the modular multilevel DC transformer based on the small-signal impedance model. The present application can calculate the broadband impedance of the DC transformer online with high precision and high efficiency under different application scenarios.

Description

Technical Field

[0001] The present application relates to the field of DC transformers, and in particular, to a method and device for online calculation of broadband impedance of a modular multilevel DC transformer. Background Art

[0002] DC grid technology can achieve large-scale DC interconnection of multiple energy bases and is an important development direction in the future DC transmission field. Due to the fast response and control characteristics of power electronic equipment, power system broadband oscillation accidents occur frequently. Small-signal impedance analysis is an effective method for studying power system broadband oscillation problems, and its key prerequisite is to obtain the impedance characteristics of power electronic equipment through impedance modeling.

[0003] As a core device for constructing a DC grid, the broadband impedance model of a high-voltage large-capacity modular multilevel DC transformer is a prerequisite for analyzing the stability of a DC grid. At present, the broadband impedance modeling technology for new energy and power electronic converters has been relatively mature, but the research on impedance modeling and stability analysis of modular multilevel DC transformers is almost blank, and most of the existing impedance measurement methods are based on electromagnetic transient simulation software for frequency sweep measurement, with low efficiency and complex algorithms. Summary of the Invention

[0004] The purpose of the present application is to provide a method and device for online calculation of broadband impedance of a modular multilevel DC transformer, which can calculate the broadband impedance of a DC transformer online with high precision and high efficiency in different application scenarios.

[0005] To achieve the above purpose, the present application provides the following solutions.

[0006] In a first aspect, the present application provides a method for online calculation of broadband impedance of a modular multilevel DC transformer, including: obtaining the relationship between various electrical quantities during the steady-state operation of the modular multilevel DC transformer based on the circuit topology structure of the modular multilevel DC transformer; establishing a power circuit model based on the relationship between various electrical quantities during the steady-state operation; establishing a control circuit model based on the input and output of the controller group of the modular multilevel DC transformer; establishing a small-signal impedance model based on the power circuit model and the control circuit model; and calculating the broadband impedance of the modular multilevel DC transformer based on the small-signal impedance model.

[0007] Second aspect, the present application provides an online calculation device for broadband impedance of a modular multilevel DC transformer, including: a signal processing unit, configured to process the time-domain signal of the modular multilevel DC transformer by using the FFT algorithm to obtain frequency-domain signals at different frequency points; a power circuit modeling unit, configured to establish a power circuit model; a control circuit modeling unit, configured to establish a control circuit model; a broadband impedance calculation board, respectively connected to the signal processing unit, the power circuit modeling unit and the control circuit modeling unit, configured to calculate the broadband impedance according to the frequency-domain signals at different frequency points, the power circuit model and the control circuit model; a data memory, connected to the broadband impedance calculation board, configured to store the calculation data of the broadband impedance calculation board; and a display, connected to the broadband impedance calculation board, configured to display the calculation data of the broadband impedance calculation board.

[0008] According to the specific embodiments provided by the present application, the present application has the following technical effects.

[0009] (1) High-efficiency and flexibility in calculation: The present application adopts efficient algorithms and calculation models, and is not restricted by specific DC transformer circuit topologies and control methods. It can calculate different power circuit models and control circuit models under different working conditions according to the requirements of the actual application scenario, without using a computer to scan impedance data point by point, realizing the high-efficiency and flexibility of broadband impedance calculation.

[0010] (2) High calculation accuracy: The present application adopts high-precision mathematical models and calculation methods, and can collect and process small-signal disturbances in real time according to the changes in the system operating conditions, so that the broadband impedance calculation results are dynamically updated and can accurately reflect the dynamic behavior of the system at different times and under different disturbances. Description of the Drawings

[0011] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings required to be used in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained according to these drawings.

[0012] Figure 1 It is a schematic flowchart of an online calculation method for broadband impedance of a modular multilevel DC transformer provided by an embodiment of the present application.

[0013] Figure 2 It is a schematic diagram of the circuit topology structure of a modular multilevel DC transformer.

[0014] Figure 3 It is a control block diagram of a modular multilevel DC transformer.

[0015] Figure 4 It is a schematic diagram of the simulation verification results of the DC transformer port model. Among them, (a) is a schematic diagram of the simulation verification results of the low-voltage side port impedance model, and (b) is a schematic diagram of the simulation verification results of the high-voltage side port admittance model.

[0016] Figure 5 It is a schematic diagram of the simulation verification results of the simplified model of the DC transformer port. Among them, (a) is a schematic diagram of the simulation verification results of the simplified impedance model of the low-voltage side port, and (b) is a schematic diagram of the simulation verification results of the simplified admittance model of the high-voltage side port.

[0017] Figure 6 It is a structural block diagram of an on-line calculation device for the broadband impedance of a modular multilevel DC transformer. Specific embodiments

[0018] Next, the technical solutions in the embodiments of the present application will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present application.

[0019] To make the above objects, features, and advantages of the present application more obvious and understandable, the present application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0020] In an exemplary embodiment, as Figure 1 shown, an on-line calculation method for the broadband impedance of a modular multilevel DC transformer is provided. This method is executed by a computer device, and specifically can be executed alone by a computer device such as a terminal or a server, or jointly executed by a terminal and a server. In the embodiments of the present application, this method is described by taking it as an example applied to a server, and includes the following steps S1 to S5.

[0021] S1: Obtain the relationships of various electrical quantities during the steady-state operation of the modular multilevel DC transformer based on the circuit topology of the modular multilevel DC transformer.

[0022] In this embodiment, only one circuit topology of the DC transformer is taken as an example for description. In practice, it can also be applied to other circuit structures, and is not limited to this topology. As Figure 2 shown, the modular multilevel DC transformer includes a high-voltage bridge arm, a common bridge arm, and a low-voltage bridge arm. The high-voltage bridge arm contains series-connected sub-modules and a bridge arm inductor. The common bridge arm contains series-connected sub-modules and a bridge arm inductor. The low-voltage bridge arm contains A number of series-connected sub-modules and an arm inductor. Both the high-voltage arm and the common arm adopt half-bridge sub-modules (HBSM), that is, they can only output a positive voltage, and the low-voltage arm adopts full-bridge sub-modules (FBSM), that is, the output voltage polarity can be positive or negative. For the convenience of narration, the output voltage of each arm sub-module valve is uniformly defined as , where , , respectively represent , two phases, , , , respectively represent the high-voltage arm, the common arm and the low-voltage arm. The current of each arm is , the capacitor voltage of the sub-module is , and the sum of the capacitor voltages of the sub-modules is ; the capacitance value of the sub-module capacitor is , the value of the arm inductor is , and the modulation coefficient of each arm is .

[0023] According to the circuit structure topology shown in Figure 2 , the dynamic characteristic relationships inside each arm of the modular multilevel DC transformer under steady-state operation can be obtained.

[0024] (1)

[0025] Where is the number of sub-modules put into each arm.

[0026] As shown in Figure 3 , the controller group of the modular multilevel DC transformer includes a half-bridge module energy balance controller, a full-bridge arm current controller and a low-voltage side DC voltage controller. The number of sub-modules put into each arm can be represented by the arm modulation voltages (common-mode AC modulation voltage, differential-mode AC modulation voltage, differential-mode DC modulation voltage) output by each controller.

[0027] (2)

[0028] Where is the number of sub-modules put into the phase high-voltage arm, is the number of sub-modules put into the phase common arm, is the number of sub-modules put into the phase low-voltage arm, is the number of sub-modules put into the phase high-voltage arm, is The number of sub - modules put into the phase - common bridge arm, is The number of sub - modules put into the phase - low - voltage bridge arm, is the differential - mode AC modulation voltage output by the half - bridge module energy balance controller, is the common - mode AC modulation voltage output by the half - bridge module energy balance controller, is the rated value of the sub - module capacitor voltage, is the differential - mode AC modulation voltage output by the full - bridge arm current controller, is the differential - mode DC modulation voltage output by the low - voltage side DC voltage controller. is the common - mode AC modulation voltage distribution coefficient.

[0029] According to Kirchhoff's voltage / current law, the relationship between the internal electrical quantities and the external DC voltage / current of the modular multilevel DC transformer can be obtained.

[0030] (3)

[0031] In the formula, 、 are the high - voltage side DC voltage and the low - voltage side DC voltage respectively, and are the high - voltage side DC current and the low - voltage side DC current respectively, is the output voltage of the high - voltage bridge arm sub - module valve, is the output voltage of the common - bridge arm sub - module valve, is the output voltage of the low - voltage bridge arm sub - module valve, is the resistance value of the arm inductor, is the high - voltage bridge arm current, is the common - bridge arm current, is the low - voltage bridge arm current, is the phase high - voltage bridge arm current, is the phase high - voltage bridge arm current, is the

[0032] S2: Establish a power circuit model based on the relationships of various electrical quantities during steady-state operation. The power circuit model includes a first constraint relationship, a second constraint relationship, a third constraint relationship, and a fourth constraint relationship. Step S2 specifically includes: performing a frequency-domain transformation on the relationships of various electrical quantities during steady-state operation to obtain a steady-state model of the power circuit; using the small-signal perturbation components of various electrical quantities and the bridge-arm modulation voltage to perform small-signal processing on the steady-state model of the power circuit to obtain a small-signal model of the power circuit; based on the small-signal model of the power circuit, determining the common-mode component of the difference in sub-module capacitor voltages between the high-voltage bridge arm and the common bridge arm and the small-signal perturbation constraint relationship with the bridge-arm modulation voltage, the high-voltage side DC voltage, and the low-voltage side DC current, which is defined as the first constraint relationship; based on the small-signal model of the power circuit, determining the differential-mode component of the low-voltage bridge arm current and the small-signal perturbation constraint relationship with the bridge-arm modulation voltage, the high-voltage side DC voltage, and the low-voltage side DC current, which is defined as the second constraint relationship; based on the small-signal model of the power circuit, determining the small-signal perturbation constraint relationship between the low-voltage side DC voltage and the bridge-arm modulation voltage, the high-voltage side DC voltage, and the low-voltage side DC current, which is defined as the third constraint relationship; based on the small-signal model of the power circuit, determining the small-signal perturbation constraint relationship between the high-voltage side DC current and the bridge-arm modulation voltage, the high-voltage side DC voltage, and the low-voltage side DC current, which is defined as the fourth constraint relationship.

[0033] In this embodiment, the power circuit of the modular multilevel DC transformer is modeled by the multi-harmonic linearization method, which mainly includes two steps: First, convert the relationships of various electrical quantities during the steady-state operation of the modular multilevel DC transformer in formulas (1)-(3) from the time domain to the frequency domain to obtain a steady-state model of the power circuit; then use the small-signal linearization method to further obtain a small-signal model of the power circuit.

[0034] First, define a seventh-order steady-state vector , which mainly includes the fundamental frequency, the second harmonic, and the third harmonic components.

[0035] (4)

[0036] Among them, " " represents the conjugate operation, is the steady-state DC component vector of variable z, respectively represent its steady-state vectors with frequencies of , and components.

[0037] Furthermore, the corresponding Toeplitz matrix is defined as formula (5).

[0038] (5)

[0039] In the formula, the symbol " " represents the Toeplitz operation.

[0040] Then, perform a frequency-domain transformation on the relationships between the electrical quantities in formulas (1)-(3) to obtain the corresponding steady-state model of the power circuit.

[0041] (6)

[0042] Among them, is the steady-state frequency-domain vector of the output voltage of each sub-module valve of the bridge arm, , , respectively represent , two phases, , , , respectively represent the high-voltage bridge arm, the common bridge arm, and the low-voltage bridge arm, is the steady-state frequency-domain vector of the number of sub-modules put into each bridge arm, is the steady-state matrix of the sub-module capacitor, is the steady-state frequency-domain vector of the capacitor voltage of each sub-module of the bridge arm, is the steady-state frequency-domain vector of the current of each bridge arm, is the steady-state frequency-domain vector of the number of sub-modules put into the high-voltage bridge arm of the is the steady-state frequency-domain vector of the differential-mode AC modulation voltage output by the energy balance controller of the half-bridge module, is the distribution coefficient, is the steady-state frequency-domain vector of the common-mode AC modulation voltage output by the energy balance controller of the half-bridge module, is the steady-state frequency-domain vector of the differential-mode DC modulation voltage output by the DC voltage controller on the low-voltage side, is the rated value of the sub-module capacitor voltage, is the steady-state frequency-domain vector of the number of sub-modules put into the common bridge arm of the is the steady-state frequency-domain vector of the number of sub-modules put into the low-voltage bridge arm of the is the steady-state frequency-domain vector of the differential-mode AC modulation voltage output by the full-bridge arm current controller, is the steady-state frequency-domain vector of the number of sub-modules put into the high-voltage bridge arm of the is the steady-state frequency-domain vector of the number of sub-modules put into the common bridge arm of the is the steady-state frequency-domain vector of the number of sub-modules put into the low-voltage bridge arm of the is the steady-state frequency-domain vector of the high-voltage side DC voltage, is the steady-state frequency-domain vector of the output voltage of the high-voltage leg sub-module valve, is the steady-state frequency-domain vector of the output voltage of the common leg sub-module valve, is the steady-state matrix of the leg inductance, is the steady-state frequency-domain vector of the high-voltage leg current, is the steady-state frequency-domain vector of the common leg current, is the steady-state frequency-domain vector of the low-voltage side DC voltage, is the steady-state frequency-domain vector of the output voltage of the low-voltage leg sub-module valve, is the steady-state frequency-domain vector of the low-voltage leg current, is the steady-state frequency-domain vector of the high-voltage side DC current, is the steady-state frequency-domain vector of the phase high-voltage leg current, is the steady-state frequency-domain vector of the phase high-voltage leg current, is the steady-state frequency-domain vector of the phase low-voltage leg current, is the steady-state frequency-domain vector of the

[0043] and The specific expressions of

[0044] (7)

[0045] In the above formula, represents a diagonal matrix, is the seventh-order identity matrix, is the fundamental angular frequency.

[0046] In this embodiment, the small-signal perturbation components of each electrical quantity and the bridge leg modulation voltage output by each controller are used to perform small-signal processing on the steady-state model of the power circuit (formula (6)) to obtain the small-signal model of the power circuit.

[0047] (8)

[0048] In the formula, the subscripts "0" and " " represent the steady-state frequency-domain component and the small-signal perturbation component respectively, is the small-signal perturbation vector of the output voltage of each bridge leg sub-module valve, is the small-signal perturbation vector of the capacitor voltage of each bridge leg sub-module, is the small-signal perturbation vector of the number of sub-modules put into each bridge leg, is the small-signal perturbation matrix of the sub-module capacitor, is the small-signal perturbation vector of the currents of each bridge arm, is the small-signal perturbation vector of the number of sub-modules put into the phase high-voltage bridge arm, is the small-signal perturbation vector of the differential-mode AC modulation voltage output by the energy balance controller of the half-bridge module, is the small-signal perturbation vector of the common-mode AC modulation voltage output by the energy balance controller of the half-bridge module, is the small-signal perturbation vector of the number of sub-modules put into the phase common bridge arm, is the small-signal perturbation vector of the number of sub-modules put into the phase high-voltage bridge arm, is the small-signal perturbation vector of the number of sub-modules put into the phase common bridge arm, is the small-signal perturbation vector of the number of sub-modules put into the phase low-voltage bridge arm, is the small-signal perturbation vector of the number of sub-modules put into the phase low-voltage bridge arm, is the small-signal perturbation vector of the high-voltage side DC voltage, is the small-signal perturbation vector of the output voltage of the valve of the high-voltage bridge arm sub-module, is the small-signal perturbation matrix of the bridge arm inductance, is the small-signal perturbation vector of the low-voltage side DC voltage, is the small-signal perturbation vector of the common bridge arm current, is the small-signal perturbation vector of the high-voltage bridge arm current, is the small-signal perturbation vector of the output voltage of the valve of the low-voltage bridge arm sub-module, is the small-signal perturbation vector of the low-voltage bridge arm current, is the small-signal perturbation vector of the high-voltage side DC current, is the small-signal perturbation vector of the phase high-voltage bridge arm current, is the small-signal perturbation vector of the phase high-voltage bridge arm current, is the small-signal perturbation vector of the phase low-voltage bridge arm current, is the small-signal perturbation vector of the

[0049] and The expressions are as follows.

[0050] (9)

[0051] In the formula,[[]] represents the small-signal perturbation angular frequency.

[0052] From formula (8), the small-signal perturbation relationships between the modulation coefficients of the high-voltage bridge arm, the common bridge arm, the DC voltage on the high-voltage side, the DC voltage on the low-voltage side, and the currents of the high-voltage bridge arm and the common bridge arm can be obtained.

[0053] (10)

[0054] Among them,[[]] is the small-signal perturbation vector of the modulation coefficient of the high-voltage bridge arm,[[]] is the small-signal perturbation vector of the modulation coefficient of the common bridge arm,[[]] is the small-signal perturbation vector of the modulation coefficient of the low-voltage bridge arm. The coefficient matrices 、 、 、 、 、 、 、 、 、 The detailed expressions are as follows.

[0055] (11)

[0056] (12)

[0057] In the above formula,[[]] 、 、 、 、 、 、 、 、 are all coefficient matrices,[[]] 、 、 are the frequency-domain vectors of the capacitor voltage of the sub-module, the current of the bridge arm, and the modulation coefficient respectively.

[0058] From the relationship between the current of the low-voltage bridge arm and the DC current on the low-voltage side in the two phases of the DC transformer in formula (8), the small-signal perturbation relationships between the modulation coefficient of the bridge arm, the DC voltage on the high-voltage side, the DC current on the low-voltage side, and the DC voltage on the low-voltage side are as follows.

[0059] (13)

[0060] Wherein, , , , , , are all coefficient matrices.

[0061] Substituting formula (13) into (10) to eliminate the variables, the small-signal perturbation constraint relationships among the arm modulation coefficient, the DC voltage on the high-voltage side, the DC current on the low-voltage side, and the arm current can be obtained as follows.

[0062] (14)

[0063] Among them, the coefficient matrix (omitting all subscripts) is expressed as follows.

[0064]

[0065] (15)

[0066] Then, substituting the relationship between the arm modulation coefficient and the arm modulation voltage in formula (8) into formula (14), formula (16) is obtained.

[0067] (16)

[0068] Wherein, , , are all coefficient matrices.

[0069] Substituting formula (16) into formula (8), the small-signal perturbation constraint relationships among the common-mode component of the difference in sub-module capacitor voltages of the high-voltage arm and the common arm, the arm modulation voltage, the DC voltage on the high-voltage side, and the DC current on the low-voltage side can be obtained as follows.

[0070] (17)

[0071] Among them, is the small-signal perturbation vector of the common-mode component of the difference in sub-module capacitor voltages of the high-voltage arm and the common arm.

[0072] The coefficient matrix - is expressed as follows.

[0073] (18)

[0074] Wherein, is the small-signal impedance matrix of the sub-module capacitor, , , , , are all coefficient matrices.

[0075] The differential-mode component of the low-voltage bridge-arm current and the small-signal disturbance constraint relationships among the bridge-arm modulation voltage, the high-voltage side DC voltage, and the low-voltage side DC current can be obtained from Equation (16).

[0076] (19)

[0077] where is the small-signal disturbance vector of the differential-mode component of the low-voltage bridge-arm current.

[0078] Coefficient matrix The expression is as follows.

[0079] (20)

[0080] Substitute the constraint relationship between the bridge-arm modulation voltage output by the controller and the number of inserted sub-modules in Equation (8) into Equation (13), and the small-signal disturbance constraint relationships among the low-voltage side DC voltage, the bridge-arm modulation voltage, the high-voltage side DC voltage, and the low-voltage side DC current are obtained as follows.

[0081] (21)

[0082] where the coefficient matrix - The expression is as follows.

[0083] (22)

[0084] In the above formula, , , , , are all coefficient matrices.

[0085] Substitute Equation (16) into the relationship between the high-voltage side DC current and the bridge-arm current in Equation (8), and the small-signal disturbance constraint relationships among the high-voltage side DC current, the bridge-arm modulation voltage, the high-voltage side DC voltage, and the low-voltage side DC current are obtained as follows.

[0086] (23)

[0087] where the coefficient matrix - The expression is as follows.

[0088] (24)

[0089] In summary, the power circuit model of the modular multilevel DC transformer can be expressed by formulas (17), (19), (21), and (23) as follows.

[0090] (25)

[0091] S3: Establish a control circuit model based on the input and output of the controller group of the modular multi-level DC transformer. The controller group includes a half-bridge module energy balance controller, a full-bridge arm current controller and a low-voltage side DC voltage controller. The control circuit model includes: a small signal frequency domain model of the half-bridge module energy balance controller, a small signal frequency domain model of the full-bridge arm current controller and a small signal frequency domain model of the low-voltage side DC voltage controller.

[0092] The half-bridge module energy balance controller establishes the small signal component of the common-mode AC modulation voltage generated by the common-mode component of the capacitor voltage difference between the high-voltage bridge arm and the common bridge arm submodule through the half-bridge module energy balance control; the full-bridge bridge arm current controller establishes the small signal component of the differential-mode AC modulation voltage generated by the low-voltage bridge arm circulating current through the full-bridge bridge arm current control; the low-voltage side DC voltage controller establishes the small signal component of the differential-mode DC modulation voltage generated by the low-voltage side DC voltage through the low-voltage side DC voltage control. After integrating the small signal components of the above bridge arm modulation voltages, the total modulation signal of each bridge arm can be obtained, thereby establishing a control circuit model.

[0093] In a specific embodiment, the modular multi-level DC transformer control structure is as follows: Figure 3 As shown in the figure, it includes three parts: half-bridge module energy balance control, full-bridge arm current control and low-voltage side DC voltage control. The half-bridge module energy balance control controls the common-mode AC modulation voltage To balance the charging and discharging energy of the submodules of the high-voltage bridge arm and the common bridge arm. The full-bridge bridge arm current control is achieved by adjusting the full-bridge submodule valve output voltage To offset the differential AC voltage output by the high-voltage bridge arm and the common bridge arm, so as to eliminate the circulating current between the low-voltage bridge arms. The low-voltage side DC voltage control adjusts the differential DC component of the voltage between the high-voltage bridge arm and the common bridge arm by tracking the changes in the DC voltage output on the low-voltage side. To maintain the stability of the DC voltage on the low voltage side. Finally, the number of bridge arm submodules turned on output by the three-level controllers is added together to obtain the total number of each bridge arm submodule turned on. Figure 3 middle, Represents the number of bridge arm submodules put into operation for the output of the low-voltage side DC voltage controller. Represents the total number of bridge arm sub-modules put into use for the controller output.

[0094] First, based on Figure 3 The small signal frequency domain model of the half-bridge module energy balance controller can be obtained.

[0095] (26)

[0096] Wherein, is the small-signal perturbation vector of the common-mode AC modulation voltage reference value, is the small-signal perturbation vector of the common-mode component reference value of the difference in sub-module capacitor voltages between the high-voltage bridge arm and the common bridge arm, , , are the transfer function matrices of the PI controller, the low-pass filter, and the cosine function respectively, and represent the transfer functions of the PI controller and the low-pass filter at the frequency of respectively.

[0097] The small-signal frequency-domain model of the full-bridge arm current controller is as follows.

[0098] (27)

[0099] Wherein, is the small-signal perturbation vector of the differential-mode AC modulation voltage reference value, is the small-signal perturbation vector of the differential-mode component reference value of the low-voltage bridge arm current, , are the transfer function matrices of the PR controller and the high-pass filter respectively, and represent the transfer functions of the PR controller and the high-pass filter at the frequency of respectively.

[0100] Similarly, the small-signal frequency-domain model of the low-voltage side DC voltage controller is as follows.

[0101] (28)

[0102] Wherein, is the small-signal perturbation vector of the differential-mode DC modulation voltage reference value, is the small-signal perturbation vector of the low-voltage side DC voltage reference value, , are the transfer function matrices of the PI controller and the low-pass filter respectively, and represent the transfer functions of the PI controller and the low-pass filter at the frequency of respectively.

[0103] S4: Establish a small-signal impedance model based on the power circuit model and the control circuit model.

[0104] In this embodiment, the power circuit model (Formula (25)) and the control circuit model (Formula (26)-Formula (28)) are combined to obtain a small signal impedance model that characterizes the dual-port dynamic characteristics of the DC transformer as follows.

[0105] (29)

[0106] In the formula, and They are the high-voltage side port admittance matrix and the low-voltage side port impedance matrix, and and Represents the coupling matrix between the high and low voltage side systems.

[0107] The detailed expressions are as follows.

[0108] (30)

[0109] Among them, the coefficient matrix The expression of is as follows.

[0110] (31)

[0111] In the above formula, , , , , , , , , , , , , , , , , , are coefficient matrices.

[0112] When the disturbance frequency is very high, due to the high-frequency filtering effect of the capacitor, the influence of the high-frequency disturbance of the sub-module capacitor voltage can be ignored. Therefore, the small signal impedance model can be greatly simplified. The simplified small signal impedance model is expressed as follows.

[0113] (32)

[0114] in, represents the simplified model of high-voltage side port admittance, Represents the simplified model of low-voltage side port impedance, represents the influence of control delay, S is the complex frequency, and L is the inductance of the bridge arm.

[0115] S5: Calculate the broadband impedance of the modular multilevel DC transformer based on the small-signal impedance model.

[0116] For the calculation method of the broadband impedance of the modular multilevel DC transformer proposed in this application, first, based on the operating condition information and circuit topology, combined with Kirchhoff's voltage / current law, a power circuit model is established; then, using the input / output signals of the controller and the transfer function of the control link, a control circuit model is established; after substituting the control circuit model into the power circuit model and eliminating the intermediate variables, a small-signal impedance model can be obtained. The steady-state signals of the modulation coefficients of each arm, arm currents, arm valve output voltages, and sub-module capacitor voltages of each phase at the corresponding frequency points are extracted in real-time using the fast Fourier transform algorithm and input into the small-signal impedance model to calculate the broadband impedance under the current operating conditions and control modes, which can be directly used for the small-signal stability analysis of the modular multilevel DC transformer, enhancing the flexibility of impedance calculation and improving the efficiency of small-signal stability analysis.

[0117] According to the content described in this application, a corresponding two-phase single-pole simulation model is built in MATLAB / Simulink according to the Figure 2 shown circuit topology, and the rated parameters of the simulation circuit are shown in Table 1.

[0118] Table 1

[0119]

[0120] To verify the correctness of this application, an electromagnetic transient simulation model of the modular multilevel DC transformer is built in Matlab / Simulink, and the high-voltage side port admittance matrix and low-voltage side port impedance matrix models are measured by point-by-point frequency scanning and compared with the analytical calculation results. The specific scanning process is as follows.

[0121] (1) Add small-signal perturbation components with a frequency of at the high-voltage side DC voltage and low-voltage side DC current respectively, and wait for the system to enter a new steady-state period.

[0122] (2) Sample the DC voltage / current and use FFT analysis to extract the Fourier coefficients of the small perturbation harmonics with a frequency of

[0123] (3) Calculate according to the definition of the small perturbation harmonic impedance described above.

[0124] (4) Change the frequency of the small-signal perturbation components added at the high-voltage side DC voltage and low-voltage side DC current and repeat steps (1) to (3) to measure the small-signal perturbation harmonic impedance values at other frequency points.

[0125] Figure 4In (a) and (b), the simulation measurement results and analytical calculation results of the low-voltage side port impedance and high-voltage side port admittance of the modular multilevel DC transformer in the frequency range of 1 to 2500 Hz are compared respectively. The red circles are the simulation calculation results, and the blue curves are the theoretical calculation results. It can be found that the high-voltage side port admittance and low-voltage side port impedance models of the modular multilevel DC transformer obtained by electromagnetic transient simulation frequency sweep measurement have high consistency with their detailed analytical models.

[0126] Figure 5 In (a) is the simulation verification result of the simplified model of the low-voltage side port impedance. Figure 5 In (b) is the simulation verification result of the simplified model of the high-voltage side port admittance. It can be seen that in the frequency range of 300 Hz and above, the simplified analytical model has high consistency with the detailed theoretical model.

[0127] The above results fully prove the effectiveness and practicability of the broadband impedance online calculation method for the modular multilevel DC transformer proposed in this application.

[0128] Based on the same inventive concept, in an exemplary embodiment, as Figure 6 shown, a broadband impedance online calculation device for a modular multilevel DC transformer is provided, including the following units.

[0129] (1) A signal processing unit, configured to process the time-domain signal of the modular multilevel DC transformer by using the FFT algorithm to obtain the frequency-domain signals at different frequency points.

[0130] The signal processing unit measures in real time the time-domain signal values of the modulation coefficients, arm currents, arm valve output voltages, and sub-module capacitor voltages of each arm in each phase of the modular multilevel DC transformer, extracts the DC component, fundamental wave, second harmonic, and third harmonic components of the corresponding signals by using the FFT algorithm, obtains the amplitudes and phase angles of the frequency-domain components of each signal, and inputs the frequency-domain signals at different frequency points into the broadband impedance calculation board.

[0131] (2) A power circuit modeling unit, configured to establish a power circuit model.

[0132] The power circuit model is determined by the DC transformer circuit topology structure in the actual application scenario and the current operating condition information, and is often imported from an external system. When performing impedance calculation, the broadband impedance calculation board directly obtains the data in the power circuit modeling unit under the current operating condition for impedance calculation and analysis.

[0133] (3) A control circuit modeling unit, configured to establish a control circuit model.

[0134] The control circuit model is established by using the small signal disturbance components of the electrical quantity input by each controller and the small signal disturbance components of the modulation voltage output. The small signal impedance model can be obtained by combining it with the power circuit model.

[0135] (4) A broadband impedance calculation board, connected to the signal processing unit, the power circuit modeling unit and the control circuit modeling unit, respectively, for calculating broadband impedance according to frequency domain signals at different frequency points, the power circuit model and the control circuit model.

[0136] The broadband impedance calculation board is the core part of this device. It is embedded with a matching broadband impedance calculation program. It is mainly responsible for calculating the impedance amplitude and phase angle data of the modular multi-level DC transformer under different disturbance frequencies based on the collected signals, power circuit modeling unit, and control circuit modeling unit data, and outputs the data to the data storage and display. The board contains a high-performance processor, dedicated calculation circuits and algorithms, which can calculate broadband impedance in real time and dynamically output it to the display.

[0137] (5) A data storage device connected to the broadband impedance calculation board and used to store calculation data of the broadband impedance calculation board.

[0138] The data storage device is used to store the impedance amplitude and phase angle calculation results of the DC transformer at different disturbance frequency points, which can be directly used for the small signal disturbance stability analysis of the modular multi-level DC transformer. It includes high-speed cache and long-term storage devices to ensure the reliability and persistence of data.

[0139] (6) A display connected to the broadband impedance calculation board and used to display the calculation data of the broadband impedance calculation board.

[0140] The display is the user interface of the device, which is mainly responsible for displaying the broadband impedance calculation results in the form of waveforms for reference and subsequent broadband stability analysis. The display includes display devices such as LCD screens and touch screens.

[0141] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of relevant data must comply with relevant regulations.

[0142] Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be completed by instructing relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above methods. Among them, any reference to a memory, database, or other medium used in the embodiments provided in the present application can include at least one of non-volatile and volatile memories. Non-volatile memories can include read-only memory (ROM), magnetic tapes, floppy disks, flash memories, optical memories, high-density embedded non-volatile memories, resistive random access memories (ReRAMs), magnetoresistive random access memories (MRAMs), ferroelectric random access memories (FRAMs), phase change memories (PCMs), graphene memories, etc. Volatile memories can include random access memory (RAM) or external cache memories, etc. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0143] The databases involved in the embodiments provided in the present application can include at least one of relational databases and non-relational databases. Non-relational databases can include distributed databases based on blockchain, etc., without limitation. The processors involved in the embodiments provided in the present application can be general-purpose processors, central processors, graphics processors, digital signal processors, programmable logics, data processing logics based on quantum computing, etc., without limitation.

[0144] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered to be within the scope described in this specification.

[0145] In this article, specific examples are used to elaborate on the principles and implementation manners of the present application. The descriptions of the above embodiments are only used to help understand the method and its core idea of the present application; at the same time, for those of ordinary skill in the art, according to the idea of the present application, there will be changes in the specific implementation manners and application scopes. In summary, the content of this specification should not be construed as a limitation to the present application.

Claims

1. A modular multi-level DC transformer broadband impedance online calculation method, characterized in that: include: Based on the circuit topology of modular multilevel DC transformer, the relationship between various electrical quantities of modular multilevel DC transformer in steady-state operation is obtained; Establish a power circuit model based on the relationship between various electrical quantities during steady-state operation; Establishing a control circuit model based on the input and output of the controller group of the modular multi-level DC transformer; Establishing a small signal impedance model based on the power circuit model and the control circuit model; Calculating the broadband impedance of the modular multi-level DC transformer based on the small signal impedance model; The modular multi-level DC transformer includes a high-voltage bridge arm, a common bridge arm and a low-voltage bridge arm; the controller group includes a half-bridge module energy balance controller, a full-bridge bridge arm current controller and a low-voltage side DC voltage controller; the power circuit model includes a first constraint relationship, a second constraint relationship, a third constraint relationship and a fourth constraint relationship; Among them, the power circuit model is established based on the relationship between various electrical quantities during steady-state operation, including: The relationship between various electrical quantities during steady-state operation is transformed into the frequency domain to obtain a steady-state model of the power circuit; The small signal disturbance component of the bridge arm modulation voltage output by each electrical quantity and the controller group is used to perform small signal processing on the steady-state model of the power circuit to obtain a small signal model of the power circuit; the bridge arm modulation voltage includes a common mode AC modulation voltage, a differential mode AC modulation voltage and a differential mode DC modulation voltage; Based on the power circuit small signal model, determine the small signal disturbance constraint relationship between the common mode component of the submodule capacitor voltage difference between the high-voltage bridge arm and the common bridge arm and the bridge arm modulation voltage, the high-voltage side DC voltage and the low-voltage side DC current, which is defined as the first constraint relationship; Based on the power circuit small signal model, determine the small signal disturbance constraint relationship between the differential mode component of the low voltage bridge arm current and the bridge arm modulation voltage, the high voltage side DC voltage and the low voltage side DC current, which is defined as the second constraint relationship; Based on the power circuit small signal model, determine the small signal disturbance constraint relationship between the low-voltage side DC voltage and the bridge arm modulation voltage, the high-voltage side DC voltage and the low-voltage side DC current, which is defined as the third constraint relationship; Based on the small signal model of the power circuit, the small signal disturbance constraint relationship between the high-voltage side DC current and the bridge arm modulation voltage, the high-voltage side DC voltage and the low-voltage side DC current is determined, which is defined as the fourth constraint relationship.

2. The online calculation method for broadband impedance of modular multi-level DC transformer according to claim 1 is characterized in that: The expression of the steady-state model of the power circuit is: ； in, is the steady-state frequency domain vector of the valve output voltage of each bridge arm submodule, , , respectively , Two phases, , , , respectively represent the high voltage bridge arm, the common bridge arm and the low voltage bridge arm, represents the Toeplitz operation, The steady-state frequency domain vector of the number of inputs to each bridge arm submodule, is the steady-state matrix of the submodule capacitance, is the steady-state frequency domain vector of the capacitor voltage of each bridge arm submodule, is the steady-state frequency domain vector of each bridge arm current, for The steady-state frequency domain vector of the number of phase high-voltage bridge arm submodules put into operation, is the steady-state frequency domain vector of the differential-mode AC modulation voltage output by the half-bridge module energy balance controller, is the common mode AC modulation voltage distribution coefficient, is the steady-state frequency domain vector of the common-mode AC modulation voltage output by the half-bridge module energy balance controller, is the steady-state frequency domain vector of the differential-mode DC modulation voltage output by the low-voltage side DC voltage controller, is the submodule capacitor voltage rating, for The steady-state frequency domain vector of the number of phase common bridge arm submodules put into operation, for The steady-state frequency domain vector of the number of phase low-voltage bridge arm submodules put into operation, is the steady-state frequency domain vector of the differential-mode AC modulation voltage output by the full-bridge arm current controller, for The steady-state frequency domain vector of the number of phase high-voltage bridge arm submodules put into operation, for The steady-state frequency domain vector of the number of phase common bridge arm submodules put into operation, for The steady-state frequency domain vector of the number of low-voltage bridge arm submodules put into operation. is the steady-state frequency domain vector of the DC voltage on the high-voltage side, is the steady-state frequency domain vector of the high-voltage bridge arm submodule valve output voltage, is the steady-state frequency domain vector of the common bridge arm submodule valve output voltage, is the steady-state matrix of the bridge arm inductance, is the steady-state frequency domain vector of the high-voltage bridge arm current, is the steady-state frequency domain vector of the common bridge arm current, is the steady-state frequency domain vector of the low-voltage side DC voltage, is the steady-state frequency domain vector of the low-voltage bridge arm submodule valve output voltage, is the steady-state frequency domain vector of the low-voltage bridge arm current, is the steady-state frequency domain vector of the DC current on the high-voltage side, for The steady-state frequency domain vector of the phase high-voltage bridge arm current, for The steady-state frequency domain vector of the phase high-voltage bridge arm current, is the steady-state frequency domain vector of the DC current on the low-voltage side, for The steady-state frequency domain vector of the phase low-voltage bridge arm current, for The steady-state frequency domain vector of the phase low-voltage bridge arm current.

3. The method for online calculation of broadband impedance of modular multi-level DC transformer according to claim 2, characterized in that: The expression of the small signal model of the power circuit is: ； in, is the small signal disturbance vector of the valve output voltage of each bridge arm submodule, is the small signal disturbance vector of the capacitor voltage of each bridge arm submodule, The number of small signal disturbance vectors input to each bridge arm submodule, is the small signal perturbation matrix of the submodule capacitance, is the small signal disturbance vector of each bridge arm current, for The small signal disturbance vector of the number of phase high voltage bridge arm submodules put into operation, is the small signal disturbance vector of the differential mode AC modulation voltage output by the half-bridge module energy balance controller, is the small signal disturbance vector of the common-mode AC modulation voltage output by the half-bridge module energy balance controller, is the small signal disturbance vector of the differential mode DC modulation voltage output by the low voltage side DC voltage controller, for The small signal disturbance vector of the number of phase common bridge arm submodules put into operation, for The small signal disturbance vector of the number of phase high voltage bridge arm submodules put into operation, for The small signal disturbance vector of the number of phase common bridge arm submodules put into operation, for The small signal disturbance vector of the number of phase low-voltage bridge arm submodules put into operation, is the small signal disturbance vector of the differential-mode AC modulation voltage output by the full-bridge arm current controller, for The small signal disturbance vector of the number of phase low-voltage bridge arm submodules put into operation, is the small signal disturbance vector of the DC voltage on the high voltage side, is the small signal disturbance vector of the high-voltage bridge arm submodule valve output voltage, is the small signal disturbance vector of the common bridge arm submodule valve output voltage is the small signal disturbance matrix of the bridge arm inductance, is the small signal disturbance vector of the DC voltage on the low voltage side, is the small signal disturbance vector of the common bridge arm current, is the small signal disturbance vector of the high voltage bridge arm current, Small signal disturbance vector of the valve output voltage of the low voltage bridge arm submodule is the small signal disturbance vector of the low voltage bridge arm current, is the small signal disturbance vector of the DC current on the high voltage side, for The small signal disturbance vector of the phase high voltage bridge arm current, for The small signal disturbance vector of the phase high voltage bridge arm current, is the small signal disturbance vector of the DC current on the low voltage side, for The small signal disturbance vector of the phase low voltage bridge arm current, for Small signal disturbance vector of the phase low-voltage bridge arm current.

4. The method for online calculation of broadband impedance of modular multi-level DC transformer according to claim 3, characterized in that: The expression of the power circuit model is: ； in, is the small signal disturbance vector of the common mode component of the capacitor voltage differential mode of the high-voltage bridge arm and the common bridge arm submodule, is the small signal disturbance vector of the differential mode component of the low voltage bridge arm current, - , - , - , - are coefficient matrices.

5. The method for online calculation of broadband impedance of modular multi-level DC transformer according to claim 1, characterized in that: The control circuit model includes: a small signal frequency domain model of a half-bridge module energy balance controller, a small signal frequency domain model of a full-bridge arm current controller, and a small signal frequency domain model of a low-voltage side DC voltage controller.

6. The method for online calculation of broadband impedance of modular multi-level DC transformer according to claim 4, characterized in that: The expression of the small signal impedance model is: ； in, is the high-voltage side port admittance matrix, , They are all coupling matrices between high and low voltage side systems. It is the low voltage side port impedance matrix.

7. The method for online calculation of broadband impedance of modular multi-level DC transformer according to claim 6, characterized in that: When the disturbance frequency exceeds the frequency threshold, the small signal impedance model is simplified to obtain a simplified small signal impedance model; The expression of the simplified small signal impedance model is: ； in, is the simplified model of the high-voltage side port admittance, Simplified model for low voltage side port impedance, represents the influence of control delay, , They are PI controller and low-pass filter at a frequency of Transfer function at , S is the complex frequency, L is the bridge arm inductance.

8. A modular multi-level DC transformer broadband impedance online calculation device, characterized in that: include: A signal processing unit, used to process the time domain signal of the modular multi-level DC transformer by using an FFT algorithm to obtain frequency domain signals at different frequency points; A power circuit modeling unit, used for establishing a power circuit model; A control circuit modeling unit, used for establishing a control circuit model based on input and output of a controller group of a modular multi-level DC transformer; A broadband impedance calculation board is connected to the signal processing unit, the power circuit modeling unit and the control circuit modeling unit respectively, and is used to calculate broadband impedance according to frequency domain signals at different frequency points, the power circuit model and the control circuit model; A data storage device connected to the broadband impedance calculation board and used to store calculation data of the broadband impedance calculation board; A display, connected to the broadband impedance calculation board, for displaying the calculation data of the broadband impedance calculation board; The modular multi-level DC transformer includes a high-voltage bridge arm, a common bridge arm and a low-voltage bridge arm; the controller group includes a half-bridge module energy balance controller, a full-bridge bridge arm current controller and a low-voltage side DC voltage controller; the power circuit model includes a first constraint relationship, a second constraint relationship, a third constraint relationship and a fourth constraint relationship; Among them, the power circuit model is established based on the relationship between various electrical quantities during steady-state operation, including: The relationship between various electrical quantities during steady-state operation is transformed into the frequency domain to obtain a steady-state model of the power circuit; The small signal disturbance component of the bridge arm modulation voltage output by each electrical quantity and the controller group is used to perform small signal processing on the steady-state model of the power circuit to obtain a small signal model of the power circuit; the bridge arm modulation voltage includes a common mode AC modulation voltage, a differential mode AC modulation voltage and a differential mode DC modulation voltage; Based on the power circuit small signal model, determine the small signal disturbance constraint relationship between the common mode component of the submodule capacitor voltage difference between the high-voltage bridge arm and the common bridge arm and the bridge arm modulation voltage, the high-voltage side DC voltage and the low-voltage side DC current, which is defined as the first constraint relationship; Based on the power circuit small signal model, determine the small signal disturbance constraint relationship between the differential mode component of the low voltage bridge arm current and the bridge arm modulation voltage, the high voltage side DC voltage and the low voltage side DC current, which is defined as the second constraint relationship; Based on the power circuit small signal model, determine the small signal disturbance constraint relationship between the low-voltage side DC voltage and the bridge arm modulation voltage, the high-voltage side DC voltage and the low-voltage side DC current, which is defined as the third constraint relationship; Based on the small signal model of the power circuit, the small signal disturbance constraint relationship between the high-voltage side DC current and the bridge arm modulation voltage, the high-voltage side DC voltage and the low-voltage side DC current is determined, which is defined as the fourth constraint relationship.

Images