An impedance modeling method for three-phase four-leg grid-connected converter

Abstract

The present invention discloses an impedance modeling method suitable for a three-phase four-bridge-arm grid-type converter, which belongs to the field of grid-type converter modeling. An output impedance model in a dq0 coordinate system is established according to the main circuit structure, a full response model in a complex frequency domain is obtained by Laplace transform, a transfer function of a small signal disturbance in a transmission path in the main circuit is written in parallel, a transfer function of the influence of a small signal disturbance on a reference angle is written in parallel according to the active power control link of a VSG, a transfer function of a small signal disturbance from a system variable to a control variable is written in parallel, a topological structure of a small signal disturbance transmission path and a signal flow graph are drawn, an output impedance model of a three-phase four-bridge-arm grid-type converter in a dq0 coordinate system is obtained by simplification of a Mersenne formula, and a positive and negative zero-sequence impedance model is obtained by an equivalent matrix. The present invention considers zero-sequence impedance in the modeling process of a three-phase four-bridge-arm grid-type converter, obtains a complete sequence impedance model, and is helpful for impedance analysis under unbalanced conditions.

Description

Technical Field

[0001] The present invention belongs to the field of grid-connected converter modeling, and in particular relates to an impedance modeling method for a three-phase four-bridge-arm grid-connected converter. Background Art

[0002] Grid-connected voltage source converters (VSC) have been widely used in power system solutions such as renewable energy generation, flexible power transmission and energy-saving electricity consumption. However, the integration of power electronic converters has brought problems such as nonlinearity, imbalance, low inertia and weak damping to traditional power grids. The three-phase four-bridge-arm inverter has the ability to solve the imbalance of three-phase power supply (load), and the virtual synchronous generator has damping and inertia characteristics. Therefore, the three-phase four-bridge-arm grid-type inverter has the ability to solve the above problems. To comprehensively analyze the stability of the three-phase four-bridge-arm grid-type inverter, it is necessary to establish its impedance model. Patent CN117313624A discloses a general sequence impedance modeling method, device, system and medium for grid-type converters, which significantly improves the efficiency of sequence impedance modeling for different grid-type converters. However, the above method does not consider zero-sequence impedance and cannot analyze stability problems under unbalanced conditions. Therefore, an impedance modeling method for a three-phase four-bridge-arm grid-type converter is needed. Summary of the invention

[0003] The technical problem to be solved by the present invention is to provide an impedance modeling method for a three-phase four-bridge-arm grid-type converter. Impedance modeling is performed by a small signal analysis method, and the topological structure of the three-phase four-bridge-arm grid-type converter is analyzed to obtain the positive and negative zero-sequence impedance model of the three-phase four-bridge-arm grid-type converter.

[0004] In order to solve the above technical problems, the technical solution adopted by the present invention is: an impedance modeling method suitable for a three-phase four-bridge-arm grid-type converter, comprising the following steps:

[0005] Step S1: Establish a main circuit output impedance model of a three-phase four-bridge-arm inverter in an abc coordinate system according to the main circuit structure, transform it to a dq0 rotating coordinate system through Clark transformation and Park transformation, and then transform it to a full response model in a complex frequency domain through Laplace transformation;

[0006] Step S2: establishing a transfer function of the transmission path of the small signal disturbance in the main circuit through a full response model of the output impedance of the main circuit;

[0007] Step S3: The disturbance value of active power is calculated according to the instantaneous power theory, and the transfer function of the influence of small signal disturbance on the reference angle is obtained through the active power control link of VSG;

[0008] Step S4: Based on the expression of the influence of the small signal disturbance on the reference angle, write the transfer function of the small signal disturbance from the system variable to the control variable;

[0009] Step S5: Draw the topological structure of the small signal disturbance transfer path through the transfer function of the small signal disturbance transfer path in the main circuit, the transfer function of the small signal disturbance from the system variable to the control variable, and the transfer function of the control structure;

[0010] Step S6: Draw a signal flow graph according to the topological structure of the small signal disturbance transmission path, and then obtain the transfer function from the voltage small signal to the current small signal according to the Mason formula, and sort out the output impedance model of the three-phase four-arm grid-type converter in the dq0 rotating coordinate system, and then convert the impedance of the dq0 domain into the impedance model of the sequence domain through the impedance equivalent.

[0011] A further improvement of the technical solution of the present invention is that: in step S1, the main circuit output impedance model of the three-phase four-bridge-arm inverter in the abc coordinate system is established according to the main circuit structure, converted to the dq0 rotating coordinate system through Clark transformation and Park transformation, and then converted to the full response model in the complex frequency domain through Laplace transformation. The structure of the main circuit is shown in Figure 2 , its output impedance model is:

[0012]

[0013] in, Represents the system value of the output voltage of the first three bridge arms of the converter, represents the system value of the filter inductor current, Indicates the system value of the voltage at the point of common connection (PCC), represents the system value of the fourth bridge arm current, R f Represents the parasitic resistance of the filter, L f Represents the filter inductance, R n Represents the parasitic resistance of the fourth bridge arm filter, L n Represents the inductance of the fourth bridge arm filter.

[0014] The output impedance model in the dq0 coordinate system is:

[0015]

[0016] in, It represents the system value of the output voltage of the first three bridge arms in the dq0 coordinate system, represents the system value of the filter inductor current in the dq0 coordinate system, Represents the system value of the common connection point (PCC) voltage in the dq0 coordinate system.

[0017] The full response model in the complex frequency domain is:

[0018]

[0019] in, represents the complex frequency domain system value of voltage in the dq0 coordinate system, represents the complex frequency domain system value of the filter inductor current in the dq0 coordinate system, Represents the complex frequency domain system value of the common connection point (PCC) voltage in the dq0 coordinate system.

[0020] A further improvement of the technical solution of the present invention is that in step S2, a transfer function of the transmission path of the small signal disturbance in the main circuit is established through the full response model of the output impedance of the main circuit. The transfer function of the transmission path of the small signal disturbance in the main circuit is:

[0021]

[0022]

[0023] Among them, U dc represents the voltage of the DC voltage source, represents the small signal disturbance system value of the duty cycle, represents the small signal disturbance system value of the filter inductor current, Represents the small signal disturbance system value of the common connection point (PCC) voltage in the dq0 coordinate system.

[0024] A further improvement of the technical solution of the present invention is that in step S3, the disturbance value of active power is calculated according to the instantaneous power theory, and the transfer function of the influence of small signal disturbance on the reference angle is obtained through the active power control link of VSG. The expression of the active power disturbance value calculated by the instantaneous power theory is:

[0025]

[0026] in, represents the small signal disturbance control value of the d-axis voltage, represents the small signal disturbance control value of the q-axis voltage, represents the small signal disturbance control value of the d-axis inductor current, Represents the small signal disturbance control value of the q-axis inductor current.

[0027] The transfer function of the small signal disturbance on the reference angle is:

[0028]

[0029]

[0030]

[0031] A further improvement of the technical solution of the present invention is that: in step S4, the transfer function of the small signal disturbance from the system variable to the control variable is listed according to the expression of the influence of the small signal disturbance on the reference angle. The expression of the reference voltage small signal transfer function is:

[0032]

[0033]

[0034]

[0035] Where, ΔV d , ΔV q , ΔV z Represents the small signal disturbance value of the reference voltage, V m Indicates the reference value of voltage amplitude.

[0036] The expression of the control voltage small signal transfer function is:

[0037]

[0038] in, Represents the small signal disturbance value of the control voltage.

[0039] The expression of the control current small signal transfer function is:

[0040]

[0041] in, Represents the small signal disturbance value of the control current.

[0042] The expression of the duty cycle small signal transfer function of the system is:

[0043]

[0044] A further improvement of the technical solution of the present invention is that: the topological structure of the small signal disturbance transmission path in step S5 is shown in the attached Figure 1 .

[0045] A further improvement of the technical solution of the present invention is that: in step S6, a signal flow graph is drawn according to the topological structure of the small signal disturbance transmission path, and then the transfer function from the voltage small signal to the current small signal is obtained according to the Mason formula, and the output impedance model of the three-phase four-arm grid-type converter in the dq0 rotating coordinate system is obtained, and then the impedance of the dq0 domain is equivalently converted into an impedance model of the sequence domain.

[0046] The expression of the output impedance model obtained according to the Mason formula is:

[0047]

[0048]

[0049] ΣL1=-G uPIR G iP G vd G dc Y out G iu +G uPIR G iP G vd G dc Y out G iv -G iP G vd G dc Y out G ii +G dc Y out G id

[0050] The expression of the sequence domain impedance model is:

[0051]

[0052]

[0053] Here, j represents an imaginary factor.

[0054] Due to the adoption of the above technical solution, the technical progress achieved by the present invention is:

[0055] 1. Through the topological structure of the three-phase four-bridge-arm grid-type converter, the positive and negative zero-sequence impedance model of the three-phase four-bridge-arm inverter is obtained. The establishment of the zero-sequence impedance model broadens the angle of stability analysis and helps to better involve system parameters.

[0056] 2. First, establish the output impedance model in the dq0 coordinate system according to the main circuit structure, and then obtain the full response model in the complex frequency domain through Laplace transform, and write the transfer function of the small signal disturbance in the main circuit. Secondly, write the transfer function of the small signal disturbance on the reference angle according to the active power control link of VSG, and write the transfer function of the small signal disturbance from the system variable to the control variable. Then draw the topological structure and signal flow graph of the small signal disturbance transmission path, simplify it through the Mason formula, and obtain the output impedance model of the three-phase four-bridge arm grid-type converter in the dq0 coordinate system. Finally, the positive and negative zero-sequence impedance model is obtained through the equivalent matrix. The present invention takes zero-sequence impedance into account in the modeling process of the three-phase four-bridge arm grid-type converter, and obtains a complete sequence impedance model, which is helpful for impedance analysis under unbalanced conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 is the topological structure of the small signal disturbance transmission path;

[0058] Figure 2 It is the topological structure of the main circuit and control circuit of a three-phase four-leg inverter. DETAILED DESCRIPTION

[0059] The present invention is further described in detail below with reference to examples:

[0060] Figure 1 The topological structure of the small signal disturbance transmission path of the present invention is applicable to the establishment process of the impedance model of the three-phase four-bridge-arm grid-type converter, which includes the following steps:

[0061] Step S1: Establish a main circuit output impedance model of a three-phase four-bridge-arm inverter in an abc coordinate system according to the main circuit structure, transform it to a dq0 rotating coordinate system through Clark transformation and Park transformation, and then transform it to a full response model in a complex frequency domain through Laplace transformation;

[0062] Furthermore, the topological structure of the main circuit is shown in Figure 2 , its output impedance model is:

[0063]

[0064] in, Represents the system value of the output voltage of the first three bridge arms of the converter, represents the system value of the filter inductor current, Indicates the system value of the voltage at the point of common connection (PCC), represents the system value of the fourth bridge arm current, R f Represents the parasitic resistance of the filter, L f Represents the filter inductance, R n Represents the parasitic resistance of the fourth bridge arm filter, Ln Represents the inductance of the fourth bridge arm filter.

[0065] The output impedance model in the dq0 coordinate system is:

[0066]

[0067] in, It represents the system value of the output voltage of the first three bridge arms in the dq0 coordinate system, represents the system value of the filter inductor current in the dq0 coordinate system, Represents the system value of the common connection point (PCC) voltage in the dq0 coordinate system.

[0068] The full response model in the complex frequency domain is:

[0069]

[0070] in, represents the complex frequency domain system value of voltage in the dq0 coordinate system, represents the complex frequency domain system value of the filter inductor current in the dq0 coordinate system, Represents the complex frequency domain system value of the common connection point (PCC) voltage in the dq0 coordinate system.

[0071] Step S2: establishing a transfer function of the transmission path of the small signal disturbance in the main circuit through a full response model of the output impedance of the main circuit;

[0072] Furthermore, the transfer function of the small signal disturbance transmission path in the main circuit is:

[0073]

[0074] Z1=R f +s·L f

[0075] Z2=ωL f

[0076] Z3=R f +3R n +s·(L f +3L n )

[0077] Among them, U dc represents the voltage of the DC voltage source, represents the small signal disturbance system value of the duty cycle, represents the small signal disturbance system value of the filter inductor current, Represents the small signal disturbance system value of the common connection point (PCC) voltage in the dq0 coordinate system.

[0078] Step S3: The disturbance value of active power is calculated according to the instantaneous power theory, and the transfer function of the influence of small signal disturbance on the reference angle is obtained through the active power control link of VSG;

[0079] Furthermore, the instantaneous power theory calculates the active power disturbance value as follows:

[0080]

[0081] in, represents the small signal disturbance control value of the d-axis voltage, represents the small signal disturbance control value of the q-axis voltage, represents the small signal disturbance control value of the d-axis inductor current, Represents the small signal disturbance control value of the q-axis inductor current.

[0082] The transfer function of the small signal disturbance on the reference angle is:

[0083]

[0084]

[0085]

[0086] Step S4: Based on the expression of the influence of the small signal disturbance on the reference angle, write the transfer function of the small signal disturbance from the system variable to the control variable;

[0087] Furthermore, the expression of the reference voltage small signal transfer function is:

[0088]

[0089]

[0090]

[0091] Where, ΔV d , ΔV q , ΔV z Represents the small signal disturbance value of the reference voltage, V m Indicates the reference value of voltage amplitude.

[0092] The expression of the control voltage small signal transfer function is:

[0093]

[0094] in, Represents the small signal disturbance value of the control voltage.

[0095] The expression of the control current small signal transfer function is:

[0096]

[0097] in, Represents the small signal disturbance value of the control current.

[0098] The expression of the duty cycle small signal transfer function of the system is:

[0099]

[0100] Step S5: Draw the topological structure of the small signal disturbance transfer path through the transfer function of the small signal disturbance transfer path in the main circuit, the transfer function of the small signal disturbance from the system variable to the control variable, and the transfer function of the control structure.

[0101] Step S6: Draw a signal flow graph according to the topological structure of the small signal disturbance transmission path, and then obtain the transfer function from the voltage small signal to the current small signal according to the Mason formula, and sort out the output impedance model of the three-phase four-arm grid-type converter in the dq0 rotating coordinate system, and then convert the impedance of the dq0 domain into the impedance model of the sequence domain through the impedance equivalent.

[0102] Furthermore, the expression of the output impedance model obtained according to the Mason formula is:

[0103]

[0104]

[0105] ΣL1=-G uPIR G iP G vd G dc Y out G iu +G uPIR G iP G vd G dc Y out G iv -G iP G vd G dc Y out G ii +G dc Y out G id

[0106] The expression of the sequence domain impedance model is:

[0107]

[0108]

[0109] Here, j represents an imaginary factor.

Claims

1. An impedance modeling method suitable for a three-phase four-bridge-arm grid-type converter, characterized in that: The steps include: Step S1: Establish a main circuit output impedance model of a three-phase four-bridge-arm inverter in an abc coordinate system according to the main circuit structure, transform it to a dq0 rotating coordinate system through Clark transformation and Park transformation, and then transform it to a full response model in a complex frequency domain through Laplace transformation; Step S2: establishing a transfer function of the transmission path of the small signal disturbance in the main circuit through a full response model of the output impedance of the main circuit; Step S3: The disturbance value of active power is calculated according to the instantaneous power theory, and the transfer function of the influence of small signal disturbance on the reference angle is obtained through the active power control link of VSG; Step S4: According to the expression of the influence of the small signal disturbance on the reference angle, write the transfer function of the small signal disturbance from the system variable to the control variable; the transfer function of the small signal disturbance from the system variable to the control variable includes the reference voltage small signal transfer function, the control voltage small signal transfer function, the control current small signal transfer function, and the system duty cycle small signal transfer function; The expression of the reference voltage small signal transfer function is: Where, ΔV d , ΔV q , ΔV z Represents the small signal disturbance value of the reference voltage, V m Indicates the reference value of voltage amplitude; The expression of the control voltage small signal transfer function is: in, Represents the small signal disturbance value of the control voltage; The expression of the control current small signal transfer function is: in, Represents the small signal disturbance value of the control current; The expression of the duty cycle small signal transfer function of the system is: Step S5: Draw the topological structure of the small signal disturbance transfer path through the transfer function of the small signal disturbance transfer path in the main circuit, the transfer function of the small signal disturbance from the system variable to the control variable, and the transfer function of the control structure; Step S6: Draw a signal flow graph according to the topological structure of the small signal disturbance transmission path, and then obtain the transfer function from the voltage small signal to the current small signal according to the Mersenne formula, sort out the output impedance model of the three-phase four-bridge arm grid-type converter in the dq0 rotating coordinate system, and then convert the impedance in the dq0 domain into an impedance model in the sequence domain through the impedance equivalent; The structure of the main circuit in step S1 includes a three-phase four-bridge-arm inverter circuit and a filter circuit, and its output impedance model is: in, Represents the system value of the output voltage of the first three bridge arms of the converter, represents the system value of the filter inductor current, Indicates the system value of the voltage at the point of common connection PCC, represents the system value of the fourth bridge arm current, R f Represents the parasitic resistance of the filter, L f Represents the filter inductance, R n Represents the parasitic resistance of the fourth bridge arm filter, L n represents the inductance of the fourth bridge arm filter; The output impedance model in the dq0 rotating coordinate system is: in, It represents the system value of the output voltage of the first three bridge arms in the dq0 coordinate system, represents the system value of the filter inductor current in the dq0 coordinate system, represents the system value of the common connection point PCC voltage in the dq0 coordinate system; The full response model in the complex frequency domain is: in, represents the complex frequency domain system value of voltage in the dq0 coordinate system, represents the complex frequency domain system value of the filter inductor current in the dq0 coordinate system, Represents the complex frequency domain system value of the common connection point PCC voltage in the dq0 coordinate system.

2. The impedance modeling method for a three-phase four-bridge-arm grid-type converter according to claim 1 is characterized in that: The transfer function of the small signal disturbance transmission path in the main circuit in step S2 is: Z1=R f +s·L f Z2=ωL f <h2 style=";text-align:left;direction:ltr">Z3=R<h2 style=";text-align:left;direction:ltr"> f <h2 style=";text-align:left;direction:ltr"> +3R<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> +s·(L<h2 style=";text-align:left;direction:ltr"> f <h2 style=";text-align:left;direction:ltr"> +3L<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> ) Among them, U dc represents the voltage of the DC voltage source, represents the small signal disturbance system value of the duty cycle, represents the small signal disturbance system value of the filter inductor current, Represents the small signal disturbance system value of the common connection point (PCC) voltage in the dq0 coordinate system.

3. The impedance modeling method for a three-phase four-bridge-arm grid-type converter according to claim 1 is characterized in that: The expression of the active power disturbance value obtained by instantaneous power theoretical calculation in step S3 is: in, represents the small signal disturbance control value of the d-axis voltage, represents the small signal disturbance control value of the q-axis voltage, represents the small signal disturbance control value of the d-axis inductor current, represents the small signal disturbance control value of the q-axis inductor current; The transfer function of the small signal disturbance on the reference angle is:

4. The impedance modeling method for a three-phase four-bridge-arm grid-type converter according to claim 1 is characterized in that: The topological structure of the small signal disturbance transfer path in step S5 is obtained by sorting out the small signal transfer function.

5. The impedance modeling method for a three-phase four-bridge-arm grid-type converter according to claim 1 is characterized in that: The expression of the output impedance model obtained according to the Mersenne formula in step S6 is: ΣL1=-G uPIR G iP G vd G dc Y out G iu +G uPIR G iP G vd G dc Y out G iv -G iP G vd G dc Y out G ii +G dc Y out G id The expression of the sequence domain impedance model is: Here, j represents an imaginary factor.

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