MMC bipolar system DC impedance modeling method and related device

Abstract

The invention discloses an MMC bipolar system direct current impedance modeling method and a related device, and belongs to the field of electrical engineering. The modeling method integrates alternating current circuit coupling, control strategy dynamic and multi-frequency harmonic interaction through a state-space equation; a proposed harmonic state space modeling framework can accurately analyze the influence of harmonic waves on direct current impedance, a theoretical basis is provided for system resonance suppression in a weak power grid scene, the influence of a converter station alternating current side coupling part in a bipolar system on a circuit equation and a modulation ratio transfer function is considered, and a state space equation of the whole converter station is obtained; according to the modeling method provided by the invention, the generation mechanism of coupling impedance is considered, an accurate mathematical model is established to represent the high-voltage direct-current power transmission system, and the high-voltage direct-current power transmission system has the advantages that the high-voltage direct-current power transmission system can be constructed; and an important foundation is laid for stability analysis of the DC side of the converter station.

Description

Technical Field

[0001] The present invention belongs to the field of electrical engineering, and in particular relates to a method for modeling direct current impedance of an MMC bipolar system and a related device. Background Art

[0002] With the rapid adoption of renewable energy and distributed generation technologies, and the continuous expansion of high-voltage direct current (HVDC) interconnections, the structure and dynamic characteristics of power systems are undergoing significant changes. HVDC transmission systems based on modular multilevel converters (MMCs) have been widely used in grid interconnections, and more such systems will be put into operation in the future. HVDC transmission systems are complex systems with multiple ports. Resonances at any AC port can be amplified by the MMC to the DC side, causing resonances in the entire DC grid. Therefore, stability analysis is essential to ensure safe system operation. However, MMCs have complex characteristics, and their multiple internal harmonics result in multi-frequency responses. To accurately model these multi-frequency responses, the harmonic state space (HSS) modeling method is introduced to describe their characteristics.

[0003] Adopting a bipolar structure similar to traditional DC transmission systems can improve the voltage level and transmission capacity of flexible DC transmission systems. In this system, one pole of the converter station consists of a complete converter, with both converters grounded via grounding electrode leads. This structure not only improves system reliability but also provides technical support for the integration of large-scale renewable energy. However, when the converter station is connected to the grid via an impedance, its AC side voltage is determined by the currents of the two MMCs. The mutual coupling between the two MMCs not only affects the expression of circuit equations but also the small signal derivation of the control part, resulting in coupling terms in the DC impedances of the two MMCs. Therefore, a method is needed to establish a DC side output impedance model for a bipolar MMC system and analyze the impact of the coupling impedance on system stability. Summary of the Invention

[0004] Based on this, the present invention aims to propose a DC impedance modeling method and related devices for an MMC bipolar system to solve the problem that coupling terms appear in the DC impedance matrix of the bipolar MMC system, affecting the stability of the system.

[0005] In a first aspect, the present invention provides a method for modeling DC impedance of an MMC bipolar system, comprising:

[0006] Establish the state space equation of a single MMC;

[0007] The state space equation of a single converter station is established based on the AC side circuit coupling relationship and the state space equation of a single MMC;

[0008] Construct a control strategy for a single MMC and introduce the control strategy of the MMCs in the same converter station into the state space equation of the converter station where the MMC is located, thus obtaining the coupled state space equation considering MMC control.

[0009] The coupled state-space equations are used to perform harmonic modeling of the converter station and the DC impedance matrix of the converter station is calculated.

[0010] Furthermore, the state space equations for a single MMC are established as follows:

[0011] Establish the circuit equation of MMC based on the voltage-current relationship of MMC;

[0012] The state space equation of MMC is established according to the circuit equation of MMC.

[0013] Furthermore, the state space equation of the MMC is established according to the circuit equation of the MMC, including:

[0014] According to the circuit equation of MMC, the state space equation of MMC in three-phase stationary coordinate system is established;

[0015] The state space equation of MMC in the three-phase stationary coordinate system is linearized to obtain the state space equation of MMC in the positive and negative sequence coordinate system.

[0016] Furthermore, the control strategy of a single MMC is constructed, and the control strategy of the MMC in the same converter station is introduced into the state space equation of the converter station where the MMC is located. The coupled state space equation considering MMC control is obtained, including:

[0017] Construct the circulating current suppression control strategy and voltage-current dual closed-loop control strategy of MMC;

[0018] Calculate the modulation ratio of MMC based on the circulating current suppression control strategy and voltage and current dual closed-loop control strategy of MMC;

[0019] Substituting the modulation ratio of the MMC into the state space equation of the converter station where the MMC is located, the coupled state space equation considering the MMC control is obtained.

[0020] Furthermore, calculating the modulation ratio of the MMC according to the circulating current suppression control strategy of the MMC includes:

[0021] The circulating current suppression control transfer function is established according to the charge transfer characteristics of the circulating current flowing in the converter station;

[0022] Substitute the circulating current suppression control transfer function into the modulation ratio expression of a single MMC in the rotating coordinate system so that the modulation ratio can be calculated based on the circulating current suppression control transfer function.

[0023] Furthermore, the modulation ratio of the MMC is calculated according to the voltage and current dual closed-loop control strategy of the MMC, including:

[0024] Let the d-axis of the first converter station control the DC voltage, the d-axis of the second converter station control the active power, and the q-axis of all MMCs control the AC voltage. Determine the control transfer function of the phase-locked loop in the rotating coordinate system.

[0025] Considering the current inner loop control and voltage outer loop control, the control transfer function of the phase-locked loop is substituted into the modulation ratio expression of a single MMC in the rotating coordinate system, so that the modulation ratio is calculated according to the voltage and current dual closed-loop control transfer function.

[0026] Furthermore, the coupled state space equation is used to perform harmonic modeling on the converter station, and the DC impedance matrix of the converter station is calculated to include:

[0027] The Toeplitz matrix is ​​introduced to shift the input frequency to the preset output frequency, and the coupled state space equation of a single converter station is converted from the time domain to the frequency domain to obtain a harmonic state space model.

[0028] The DC impedance matrix of the converter station is calculated based on the harmonic matrix of the harmonic state space model.

[0029] In a second aspect, the present invention provides a MMC bipolar system DC impedance modeling device, comprising:

[0030] A first state space modeling module is used to establish a state space equation for a single MMC;

[0031] The second state space modeling module is used to establish the state space equation of a single converter station based on the AC side circuit coupling relationship and the state space equation of a single MMC;

[0032] The coupling modeling module is used to construct the control strategy of a single MMC. The control strategy of the MMC in the same converter station is introduced into the state space equation of the converter station where the MMC is located, and the coupled state space equation considering the MMC control is obtained.

[0033] The DC impedance calculation module is used to perform harmonic modeling of the converter station using coupled state-space equations and calculate the DC impedance matrix of the converter station.

[0034] In a third aspect, the present invention provides an electronic device comprising a memory storing computer-executable instructions and a processor, wherein when the computer-executable instructions are executed by the processor, the device executes the various steps of the MMC bipolar system DC impedance modeling method provided in the first aspect.

[0035] In a fourth aspect, the present invention provides a readable storage medium storing a computer executable program, which, when executed, can implement the various steps of the MMC bipolar system DC impedance modeling method provided in the first aspect.

[0036] Compared with the prior art, the present invention has the following beneficial effects:

[0037] The present invention proposes a DC impedance modeling method for an MMC bipolar system, which comprehensively integrates AC circuit coupling, control strategy dynamics and multi-frequency harmonic interactions through state-space equations, breaking through the limitations of traditional models in simplifying the complex dynamics within the MMC; the proposed harmonic state-space modeling framework can accurately analyze the impact of harmonics on DC impedance, providing a theoretical basis for system resonance suppression in weak power grid scenarios; the designed circulating current suppression strategy effectively suppresses the second harmonic component in the circulating current, thereby improving the system operation reliability; the influence of the AC side coupling part of the converter station in the bipolar system on the circuit equation and the modulation ratio transfer function is considered, and the state-space equation of the entire converter station is obtained; the relationship between the input variables and the state variables in the harmonic state-space equation is used to finally extract the DC impedance matrix of the converter station of the bipolar system. The modeling method proposed in the present invention takes into account the generation mechanism of the coupling impedance, establishes an accurate mathematical model to characterize the high-voltage DC transmission system, and lays an important foundation for the stability analysis of the DC side of the converter station. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0039] Figure 1 A block diagram of the MMC bipolar system structure provided by an embodiment of the present invention;

[0040] Figure 2 Flowchart of the implementation of the DC impedance modeling method for an MMC bipolar system provided by an embodiment of the present invention;

[0041] Figure 3 A schematic structural diagram of a DC impedance modeling device for an MMC bipolar system provided in an embodiment of the present invention;

[0042] Figure 4 This is a diagram of the electronic device architecture provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0043] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0044] See Figure 1 One embodiment of the present invention provides a bipolar MMC high-voltage direct current transmission system, comprising two converter stations, each of which includes two identical MMC converters, and the converter stations are connected by a 400km overhead transmission line.

[0045] For a single three-phase MMC, the following variable definitions are given:

[0046] and Represent the AC grid voltage and the three-phase voltage at the grid connection point, is the DC side neutral point voltage to ground, and the DC side voltage is , the three-phase voltage of the upper bridge arm is , the three-phase current of the upper bridge arm is , the three-phase voltage of the lower bridge arm , the three-phase current of the lower bridge arm is , the average capacitor voltage of the upper bridge arm submodule is , the average capacitor voltage of the lower bridge arm submodule is , the modulation ratio of the upper bridge arm is , the modulation ratio of the lower bridge arm is , Represents the AC impedance of the power grid. Each bridge arm contains N capacitors. The submodule and an inductor are The reactor has a resistance of .

[0047] See Figure 2 ,by Figure 1 Taking the illustrated MMC bipolar system as an example, an embodiment of the present invention provides a DC impedance modeling method for the MMC bipolar system, comprising the following steps:

[0048] Step S210: Establish the state space equation of a single MMC.

[0049] For three-phase MMC, consider the relationship between the bridge arm voltage and the equivalent capacitor, as well as the relationship between the equivalent capacitor voltage and the bridge arm current:

[0050]

[0051] AC side three-phase common mode current that circulates within the MMC bridge arm but does not appear on the AC terminals Expressed as:

[0052]

[0053] AC side differential mode current It can be calculated as:

[0054]

[0055] According to Kirchhoff's law, the voltage on the MMC AC terminal and the current and voltage on the bridge arm have the following relationship:

[0056]

[0057] Based on the above relationship, assuming that the capacitor voltages of each bridge arm are balanced and the influence of high-order switching harmonics is ignored, an average value model is established. The state space equation of a single MMC in the three-phase stationary coordinate system (abc coordinate system) is:

[0058]

[0059] Where L mac is the common mode current i gabc The equivalent inductance flowing through is (0.5L m +L t ), L t is the transformer inductance, and the matrix form of each electrical quantity is expressed as follows:

[0060]

[0061] In order to more clearly reflect the coupling relationship between different subharmonics, the state space equation of the above single MMC is converted from the three-phase stationary coordinate system to the positive and negative sequence coordinate system (pn coordinate system). The state space equation of a single MMC in the pn coordinate system is as follows:

[0062]

[0063] Among them, v DC Indicates the DC side voltage, v gpn0 Indicates the voltage at the grid connection point on the AC side, v cupn0 Represents the upper bridge arm voltage, v clpn0 Represents the lower bridge arm voltage, i gpn0 Indicates the AC side current, i cpn0 represents the common mode current, n upn0 Indicates the modulation ratio of the upper bridge arm, n lpn0 The electrical quantities are defined in the pn coordinate system and are distinguished from the aforementioned three-phase stationary coordinate system (abc coordinate system) by the subscript pn0.

[0064] For a three-phase three-wire system, there is no zero-sequence current flow path on the AC side of the MMC, and the voltage After linearization, we get , which is to force the system AC side of the small signal current to have no zero sequence component. Similarly, the following electrical quantities The form represents the linearized small signal form of the electrical quantity.

[0065] In order to simplify the analysis, a matrix C is introduced into the state space equation in the pn coordinate system. z :

[0066]

[0067] The state space equation in the above pn coordinate system is linearized, and the final small signal state space equation of a single MMC in the pn coordinate system is expressed as follows:

[0068]

[0069] Step S220: Establish a state space equation of a single converter station according to the AC side circuit coupling relationship and the state space equation of a single MMC.

[0070] observe Figure 1 It can be seen that the grid connection point of a single converter station in the bipolar MMC system is connected to the ideal grid through the same AC impedance, so the grid connection point voltage v gpn0 The size of is determined by the current of the two MMCs.

[0071]

[0072] Where, and are the grid connection point voltages of converter station 1 and converter station 2, and They represent the equivalent impedances of the grid connection points of converter stations 1 and 2 respectively, , , , are the grid-connected point currents of converters MMC1-MMC4 respectively. Based on the above expressions, the state space equation of a single MMC can be written as follows:

[0073]

[0074]

[0075]

[0076]

[0077]

[0078] From the expression of the above state-space equation, it can be seen that the elements in each matrix representation on the right side of the equation are 3*3 matrices. After substituting into each matrix representation, each addition term on the right side of the equation is a matrix with 12 rows and 1 column.

[0079] The elements in the diagonal matrix representation of the variables with the subscript pn0 above represent the positive sequence components, negative sequence components and zero sequence components in the pn coordinate system, with For example, the elements in its matrix representation 、 、 They represent the positive-sequence component, negative-sequence component and zero-sequence component of the modulation ratio respectively. The other variables are explained in the same way and will not be repeated here.

[0080] Considering the influence of the AC side circuit coupling of the bipolar MMC system, there is also a coupling coefficient matrix A sc , the expression is:

[0081]

[0082] After considering only circuit coupling, the state space equations of converter station 1 (including MMC1 and MMC2) and converter station 2 (including MMC3 and MMC4) are the same. Taking converter station 1 as an example, its state space equation can be expressed as:

[0083]

[0084] in is the state variable of converter station 1, is the derivative of the state variable of converter station 1. Δn pn0s1 represents the modulation ratio change of the MMC bridge arm in converter station 1, Δv DCs1 A represents the DC side voltage change of the MMC in converter station 1. s1 and A s2 are the state matrices of MMC1 and MMC2 in converter station 1, A sc1 and A sc2 are the coupling coefficient matrices between MMC1 and MMC2, M mmc1 and M mmc2 are the M matrices of MMC1 and MMC2 respectively (refer to the M matrix in the state space equation when modeling a single MMC above), B1 and B2 are the input matrices of MMC1 and MMC2 respectively.

[0085] The state variables of converter station 1 and converter station 2 are represented by Δx pn0s1 and Δx pn0s2 , expressed as:

[0086]

[0087] Among them, the subscripts 01 to 04 correspond to MMC1 to MMC4, and the subscripts s1 and s2 represent converter station 1 and converter station 2 respectively.

[0088] Step S230: Construct a control strategy for a single MMC, introduce the control strategy of the MMC in the same converter station into the state space equation of the converter station where the MMC is located, and obtain a coupled state space equation considering MMC control.

[0089] In order to establish a complete MMC small signal model, its control part needs to be considered during modeling. The control of MMC mainly includes circulating current suppression control and voltage and current dual closed-loop control.

[0090] Circulating current flows in the bridge arm, profoundly affecting the dynamic characteristics of the MMC. For a single MMC, to achieve circulating current suppression, the following describes an exemplary implementation based on a proportional resonant (PR) controller.

[0091] Circulating currents are primarily composed of even-order harmonics, with the second harmonic component dominating and representing a negative-sequence current. The control strategy suppresses this harmonic by setting the reference value to zero. The controller acts on the common-mode component of the phase leg's upper and lower arm modulation functions and superimposes the output with the same sign onto these upper and lower arm modulation functions, achieving circulating current suppression.

[0092]

[0093] in, represents the transfer function matrix of the circulating current suppression controller, Represents the common mode current in the pn coordinate system Transfer function matrix The obtained modulation ratio change is represents the transfer function of the PR controller, k ccp and k ccr are the proportional gain coefficient and the resonant gain coefficient, represents the damping ratio, represents the natural frequency, and s is the Laplace operator.

[0094] The control system is established in the dq coordinate system, and the phase-locked loop is used to track the q-axis voltage to achieve phase synchronization. In this embodiment of the present invention, the d-axis of MMC1 and MMC2 controls the DC voltage, and the d-axis of MMC3 and MMC4 uses P ac Control, the q-axes of the four MMCs all control the AC voltage.

[0095] The transfer function of the phase-locked loop is:

[0096]

[0097] k pllp and k plli They represent the proportional gain and integral gain of the PI controller respectively.

[0098] When the system is in steady state, the controller-side dq coordinate system determined by the phase-locked loop coincides with the system-side dq coordinate system. The presence of voltage disturbances will cause deviations in the angle extracted by the phase-locked loop, thereby affecting the transformation between the dq coordinate systems.

[0099] Specifically, the disturbance voltage, disturbance current and output voltage of the controller in the dq coordinate system are:

[0100]

[0101] In the dq coordinate system, per-unit value is used for control, where G pll (s) represents the transfer function of the phase-locked loop, G plli (s), G pllv (s) and G plln (s) represents the transfer function matrix of the phase-locked loop on the current, voltage and modulation ratio in the dq coordinate system, N 1ds and N 1qs is the steady-state value of the modulation ratio in the dq coordinate system, I ds and I qs is the steady-state value of the current in the dq coordinate system, V ds and V qs is the steady-state value of voltage in the dq coordinate system. 1dc , Δn 1qc , Δi dc , Δi qc , Δv dc and Δv qc is the small disturbance electrical quantity in the controller dq coordinate system, Δn 1d , Δn 1q , Δi d , Δi q , Δv d and Δv q It is a small disturbance electrical quantity in the system dq coordinate system.

[0102] In order to derive the expression of the simplified matrix, the following matrix is ​​defined:

[0103]

[0104] Among them G D (s) represents the decoupling part between the d-axis and the q-axis in the current loop, ω0 is the rated angular frequency of the system, G iPI (s) is the transfer function of the PI controller in the current inner loop, where k pi and k ii They represent the proportional gain and integral gain of the current inner loop PI controller respectively.

[0105] When only the inner current loop is considered, the output modulation ratio change in the dq coordinate system on the system side is expressed as:

[0106]

[0107] Δi dq and Δv dq are the small disturbances of current and voltage in the system dq coordinate system respectively.

[0108] The outer rings of the q-axis of the four MMCs are all V ac Control, q-axis reference current and its linearized small signal form The expression is:

[0109]

[0110]

[0111]

[0112] Where Δv dqc is the small disturbance of the voltage in the controller dq coordinate system, G acPI (s) represents the transfer function of the PI controller in the q-axis voltage outer loop, and They represent the proportional gain and integral gain of the q-axis voltage outer loop PI controller, is the given AC voltage reference value, G vLPF represents the transfer function of the low-pass filter in the voltage outer loop, T v is the time constant of the low-pass filter, is the q-axis voltage outer loop from arrive The transfer function of Written in 2×2 matrix form.

[0113] The d-axis outer loop of MMC1 and MMC2 controls the DC voltage , reference current and its linearized small signal form The expression is:

[0114]

[0115]

[0116] Where G dcPI (s) represents the transfer function of the d-axis voltage outer loop PI controller, and They represent the proportional gain and integral gain of the d-axis voltage outer loop PI controller, is a given DC voltage reference value. To facilitate the calculation of G dcPI(s) is written in the form of a 2×2 matrix.

[0117] According to the current inner loop control and the above outer loop control method, the expression of the MMC1 modulation ratio change is as follows:

[0118]

[0119] Where Δi dq1 and Δv dq1 represents the small disturbance of current and voltage in the dq coordinate system of the MMC1 system side, G vdq1 , G idq1 and G vdc Respectively represent the dq1 , Δv dq1 and Δv DC1 to Δn 1dq1 The transfer function matrix of .

[0120] Depend on Figure 1 It can be seen that in the dq control system, the grid connection point voltage of the converter station in the bipolar MMC system is also determined by the current of the two MMCs. The grid connection point voltage change of converter stations 1 and 2 is expressed as follows:

[0121]

[0122] Where Δi dq2 , Δi dq3 and Δi dq4 They represent the small disturbances of the current in the system side dq coordinate system of MMC2, MMC3 and MMC4 respectively.

[0123] Considering that the modulation ratio of converter MMC1 includes not only the AC side current of MMC1 itself but also the AC side current of MMC2, the modulation ratio change of MMC1 is The expression is as follows:

[0124]

[0125] Where G idq1 and G idq2 is the current Δi from the MMC in the dq coordinate system dq1 and Δi dq2 to Δn 1dq1 The transfer function, G vdc From Δv DC to Δn 1dq1 The transfer function, G idq1 and G idq2 They are all 2×2 matrices, and their matrix elements are defined as G nidd1 , G nidq1 , G niqd1 , G niqq1, G nidd2 , G nidq2 , G niqd2 and G niqq2 , which facilitates subsequent transfer to the pn coordinate system.

[0126] The expression of MMC2 modulation ratio can be obtained in the same way.

[0127] The outer ring of the d-axis of MMC3 and MMC4 adopts P ac Control, its reference current and its linearized small signal form The expression is:

[0128]

[0129] Where G pacPI (s) represents the transfer function of the d-axis power outer loop PI controller, k ppac and k piac They represent the proportional gain and integral gain of the PI controller of the d-axis power outer loop, G pLPF (s) represents the transfer function of the low-pass filter of the power outer loop, T p is the time constant of the low-pass filter, is the given AC power reference value, P ac is the active power, P ac and its linearized small signal form Δp ac The calculation is as follows:

[0130]

[0131]

[0132] Where i dc 、i qc represents the current in the controller dq coordinate system, v dc and v qc is the voltage of the controller in the dq coordinate system. and They are the d-axis power outer ring from and arrive The transfer function of .

[0133] According to the current inner loop control and the above outer loop control, the expression of the MMC3 modulation ratio change can be obtained as follows:

[0134]

[0135] Where Δv dq3 G represents the small voltage disturbance in the dq coordinate system of the MMC3 system side. vdq3is the dq coordinate system from Δv dq3 to Δn 1dq3 The transfer function of G idq3 and G idq4 is the dq coordinate system from Δi dq3 and Δi dq4 to Δn 1dq3 The transfer function, G idq3 and G idq4 They are all 2×2 matrices, and their matrix elements are defined as G nidd3 , G nidq3 , G niqd3 , G niqq3 , G nidd4 , G nidq4 , G niqd4 and G niqq4 , which facilitates subsequent transfer to the pn coordinate system.

[0136] The expression of MMC4 modulation ratio can be obtained in the same way.

[0137] The above transfer functions are established in the dq coordinate system. After the transfer functions are converted, they are expressed in the pn coordinate system as follows:

[0138]

[0139] Where G dd 、 、 and The matrix G idq1 , G idq2 , G idq3 and G idq4 The transfer function corresponding to the subscript position in G idq1 , G idq2 , G idq3 and G idq4 Transformed into the pn coordinate system, they are expressed as: G ipn01 , G ipn02 , G ipn03 and G ipn04 .

[0140] The expression of the modulation ratio change of MMC1 and MMC3 in the pn coordinate system is:

[0141]

[0142] Where Δn 1pn01 and Δn 1pn03 The first number 1 in the subscript indicates the modulation ratio under dual closed-loop control, and the following numbers 01 and 03 indicate MMC1 and MMC3 respectively. ipn01 and G ipn02 Gidq1 and G idq2 In the pn coordinate system, from Δi gpn01 and Δi gpn02 to Δn 1pn01 The transfer function, G vdc1 is the pn coordinate system from Δv dc to Δn 1pn01 The transfer function, G ipn03 and G ipn04 G idq3 and G idq4 In the pn coordinate system, from Δi gpn03 and Δi gpn04 to Δn 1pn03 The transfer function, Δi gpn01 , Δi gpn02 , Δi gpn03 and Δi gpn04 They respectively represent the changes in the AC side current of MMC1, MMC2, MMC3 and MMC4 in the pn coordinate system.

[0143] Taking MMC1 as an example, the change in its total modulation ratio Δn pn01 Including dual closed-loop control and internal circulation suppression control, it is divided into upper bridge arm and lower bridge arm. According to the above analysis, it can be expressed as:

[0144]

[0145]

[0146] Where Δn upn01 and Δn upn01 Represent the modulation ratio of the upper and lower bridge arms of MMC1, which includes the transfer function G of the circulating current suppression control part. ccpn01 And the transfer function G of the double closed-loop control part ipn01 , G ipn02 ;M 11 、M DC1 and M 12 Respectively represent the pn01 , Δv DC1 and Δx pn02 to Δn pn01 The transfer function, Δx pn01 , Δv DC1 and Δx pn02 They represent the state variables of MMC1, the DC side voltage of MMC1 and the state variables of MMC2, G vdc1 is the pn coordinate system from Δv dc to Δn 1pn01 The transfer function of .

[0147] Similarly, the MMC2 modulation ratio change Δn can be obtained pn02 The expression:

[0148]

[0149] Where M 22 、M DC2 and M 21 Represents the pn02 , Δv DC2 and Δx pn01 to Δn pn02 The transfer function, Δv DC2 Indicates the DC side voltage change of MMC2.

[0150] The modulation ratio disturbance Δn of converter station 1 (including MMC1 and MMC2) is pn0s1 The expression is:

[0151]

[0152] Similarly, the change in the MMC3 modulation ratio Δn pn03 Including dual closed-loop control and internal circulation suppression control, it is divided into the modulation ratio of the upper bridge arm and the lower bridge arm. According to the above analysis, it can be expressed as:

[0153]

[0154]

[0155] Where Δn upn03 and Δn upn03 Represents the modulation ratio change of the upper and lower bridge arms of MMC3, and also includes the transfer function G representing the circulating current suppression control ccpn03 and represents the transfer function G of the double closed-loop control ipn03 , G ipn04 , M 33 and M 34 Represents the pn03 and Δx pn04 to Δn pn03 The transfer function, Δx pn03 and Δx pn04 Represents the state variables of MMC3 and MMC4 respectively.

[0156] Similarly, we can get the Δn of MMC4 4pn0 The expression:

[0157]

[0158] Where M 44 and M 43 Represents thepn04 and Δx pn03 to Δn pn04 The transfer function of .

[0159] Modulation ratio disturbance Δn of converter station 2 (including MMC3 and MMC4) pn0s2 The expression is:

[0160]

[0161] Specifically, the state space equation of converter station 1 (including MMC1 and MMC2) obtained by considering circuit coupling and control coupling is as follows:

[0162]

[0163] The modulation ratio change Δn of converter station 1 pn0s1 Substitute the expression of into the above formula to get the following expression:

[0164]

[0165] Where A alls1 and B alls1 The state variable Δx of the slave converter station 1 is obtained after considering circuit coupling and control coupling. pn0s1 and input variable Δv DCs1 arrive The transfer function between them, the transfer function matrix A alls1 The non-diagonal terms are the coupling parts between MMC1 and MMC2.

[0166] The state space equation of converter station 2 (including MMC3 and MMC4) obtained by considering circuit coupling and control coupling is as follows:

[0167]

[0168] in, is the state variable of converter station 2, is the derivative of the state variable of converter station 2. pn0s2 represents the modulation ratio of the MMC bridge arm in converter station 2, Δv DCs2 Indicates the DC side voltage of the MMC in converter station 2. A s3 and A s4 is the state matrix of MMC3 and MMC4 in converter station 2, A sc3 and A sc4 is the coupling coefficient matrix between MMC3 and MMC4 in converter station 2, M mmc3 and M mmc4 is the M matrix of MMC3 and MMC4, B3 and B4 are the input matrices of MMC3 and MMC4.

[0169] Similarly, the modulation ratio change Δn of converter station 2 is introduced pn0s2 Substitute the expression of into the above formula to get the following expression:

[0170]

[0171] Where A alls2 and B alls2 The state variable Δx of the slave converter station 2 is obtained after considering circuit coupling and control coupling. pn0s2 and input variable Δv DCs2 arrive The transfer function between them, the transfer function matrix A alls2 The non-diagonal terms are the coupling parts between MMC3 and MMC4.

[0172] Step S440: Use the coupled state-space equation to perform harmonic modeling on the converter station and calculate the DC impedance matrix of the converter station.

[0173] MMC has multiple internal harmonics, which leads to complex internal dynamics and multi-frequency response. In order to accurately simulate the multi-frequency response and include all internal harmonic dynamics using MMC, a harmonic state space modeling approach is adopted.

[0174] The introduction of Toeplitz matrix can shift the input frequency to a set of appropriate output frequencies, thereby fully describing the frequency coupling characteristics of linear time periodic systems.

[0175] All state variables in the state-space equations are periodic signals in steady state, and the MMC is essentially considered a time-periodic system. Based on the harmonic state-space modeling method, the time-domain state-space equations of converter stations 1 and 2 can be transformed into small-signal harmonic state-space models, expressed as:

[0176]

[0177] According to the general equation of the harmonic state space, the Fourier expansion of the above equations can be written as:

[0178]

[0179] represents the Toeplitz matrix, and The harmonic state space matrices for converter stations 1 and 2 reflect the relationship between input variables and state variables. The higher the harmonic order considered in the model, the better the MMC modeling accuracy. After considering the fourth harmonic, the accuracy of the MMC impedance model can be guaranteed, as shown in the following formula:

[0180]

[0181] In the formula, the superscripts of matrix elements represent different subharmonic components.

[0182] Q is a diagonal matrix representing frequency information:

[0183]

[0184] In the pn coordinate system, the common mode current disturbance Δi at the DC end of the MMC is cpn0 is the state variable matrix Δx pn0 As a part of the MMC DC side current is 3 times the circulating current zero sequence component, and Δv DC is the input matrix, so it can be obtained from the matrix H hsss1 and H hsss2 Extract the small signal DC impedance matrix Z of converter station 1 and converter station 2 from MMCDCs1 and Z MMCDCs2 :

[0185]

[0186] In the above formula, Z DC11s1 and Z DC22s1 is the diagonal impedance of converter station 1, Z DC11s2 and Z DC22s2 is the diagonal impedance of converter station 2. DC12s1 and Z DC21s1 is the coupling impedance generated by the coupling at converter station 1, Z DC12s2 and Z DC21s2 is the coupling impedance generated by the converter station 2 taking coupling into consideration.

[0187] According to the above formula, the size of the coupling impedance is related to the size of the AC side impedance, so the change of the coupling impedance can be analyzed by changing the size of the power grid strength.

[0188] The above disclosed embodiments describe in detail a method for modeling the DC impedance of an MMC bipolar system. The disclosed method can be implemented using various devices. Therefore, the present invention also discloses a modeling device corresponding to the above method. Specific embodiments are given below for detailed description.

[0189] like Figure 3 As shown, one embodiment of the present invention provides a MMC bipolar system DC impedance modeling device, comprising:

[0190] A first state space modeling module 302 is used to establish a state space equation for a single MMC;

[0191] A second state space modeling module 304 is configured to establish a state space equation for a single converter station based on the AC side circuit coupling relationship and the state space equation for a single MMC;

[0192] The coupling modeling module 306 is used to construct a control strategy for a single MMC, introduce the control strategy of the MMC in the same converter station into the state space equation of the converter station where the MMC is located, and obtain a coupled state space equation considering MMC control;

[0193] The DC impedance calculation module 308 is used to perform harmonic modeling on the converter station using the coupled state-space equations to calculate the DC impedance matrix of the converter station.

[0194] The device provided in the embodiment of the present application has the same implementation principle and technical effects as those in the aforementioned method embodiment. For the sake of brief description, for matters not mentioned in the device embodiment, reference can be made to the corresponding content in the aforementioned method embodiment.

[0195] The methods and related devices mentioned in the above embodiments are described with reference to the method flow charts and / or structural diagrams provided in the embodiments of the present application. Specifically, each process and / or block in the method flow charts and / or structural diagrams, as well as the combination of processes and / or blocks in the flow charts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the steps in the process. Figure 1 Schematic diagram of one or more processes and / or structures Figure 1 These computer program instructions can also be stored in a computer-readable memory that can guide a computer or other programmable data processing device to work in a specific way, so that the instructions stored in the computer-readable memory produce a product including the instruction device, which implements the function specified in the process. Figure 1 Schematic diagram of one or more processes and / or structures Figure 1 These computer program instructions can also be loaded onto a computer or other programmable data processing device, so that a series of operation steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process in the process. Figure 1 The flow or flows and / or structures illustrate the steps of the functions specified in one block or multiple blocks.

[0196] The following embodiments illustrate this method using a computer device as an example. It is understood that the computer device may be any device with computing and processing capabilities, including, but not limited to, a server or a personal laptop. In one embodiment, the computer device may be an application server, which may be a server for running the application under test.

[0197] See Figure 4 , which shows a hardware block diagram of an electronic device, which is intended to represent various forms of digital computers, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. The electronic device may also represent various forms of mobile devices, such as personal digital assistants, cellular phones, smart phones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely examples and are not intended to limit the implementation of the present application described and / or claimed herein.

[0198] like Figure 4 As shown, the electronic device includes: at least one processor 1, at least one communication interface 2, at least one memory 3 and at least one communication bus 4;

[0199] In the embodiment of the present application, the number of the processor 1, the communication interface 2, the memory 3, and the communication bus 4 is at least one, and the processor 1, the communication interface 2, and the memory 3 communicate with each other through the communication bus 4;

[0200] The processor 1 may be a central processing unit (CPU), or an application-specific integrated circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of the present invention;

[0201] The memory 3 may include a high-speed RAM memory, and may also include a non-volatile memory (non-volatile memory), such as at least one disk memory;

[0202] The memory stores a program, and the processor can call the program stored in the memory, wherein the program is used to implement each processing flow of the aforementioned MMC bipolar system DC impedance modeling method.

[0203] An embodiment of the present invention further provides a readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the processing flow of the MMC bipolar system DC impedance modeling method provided in the above embodiment and / or any possible implementation method in combination with the embodiment is implemented.

[0204] The above embodiments have described the invention in particular detail with respect to possible scenarios, and those skilled in the art will recognize that the invention can be practiced through other embodiments. The specific naming of components, capitalization of terms, attributes, data structures, or any other programming or structural aspects are not mandatory or important, and the mechanisms or features of the invention may have different names, forms, or procedures. The system may be implemented through a combination of hardware and software (as described), entirely through hardware elements, or entirely through software elements. The specific division of functions between the various system components described herein is exemplary only and not mandatory; rather, the functions performed by a single system component may be performed by multiple components, or the functions performed by multiple components may be performed by a single component.

[0205] Those skilled in the art will appreciate that the various steps of the method disclosed above can be implemented by a general-purpose computing device. They can be centralized on a single computing device or distributed across a network of multiple computing devices. Alternatively, they can be implemented using program code executable by a computing device, so that they can be stored in a storage device and executed by the computing device, or they can be fabricated into separate integrated circuit modules, or multiple modules or steps can be fabricated into a single integrated circuit module for implementation. Thus, the embodiments disclosed herein are not limited to any specific combination of hardware and software.

[0206] The programs executable by these computing devices (also referred to as programs, software, software applications, or code) include machine instructions for programmable processors and can be implemented using high-level procedural and / or object-oriented programming languages, and / or assembly / machine languages. As used herein, the terms "machine-readable medium" and "computer-readable medium" refer to any computer program product, apparatus, and / or device (e.g., a magnetic disk, an optical disk, a memory, a programmable logic device (PLD)) for providing machine instructions and / or data to a programmable processor, including a machine-readable medium that receives machine instructions as a machine-readable signal. The term "machine-readable signal" refers to any signal for providing machine instructions and / or data to a programmable processor.

[0207] Certain aspects of the present invention include the process steps and instructions described herein in the form of algorithms. It should be noted that the process steps and instructions of the present invention can be implemented in software, firmware and / or hardware, and when implemented in software, they can be downloaded, stored on different platforms used by various operating systems, and operated from the platforms.

[0208] Those skilled in the art will understand that the structures shown in the accompanying drawings are merely block diagrams of partial structures related to the scheme of the present application, and do not constitute a limitation on the terminal device to which the scheme of the present application is applied. The specific terminal device may include more or fewer components than shown in the figure, or combine certain components, or have a different arrangement of components.

[0209] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "possible design" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine different embodiments or examples described in this specification and features of different embodiments or examples, unless they are mutually inconsistent.

[0210] Finally, it should be noted that, in this document, relational terms such as first and second, etc., are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or device comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or device. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of additional identical elements in the process, method, article, or device comprising the element.

[0211] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments can still be modified, or some of the technical features thereof can be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for modeling the DC impedance of an MMC bipolar system, characterized in that: include: Establish the state space equation of a single MMC; The state space equation of a single converter station is established based on the AC side circuit coupling relationship and the state space equation of a single MMC; Construct a circulating current suppression control strategy and a voltage-current dual closed-loop control strategy for a single MMC. Calculate the MMC modulation ratio based on these strategies. Substitute the MMC modulation ratio into the state-space equation of the converter station where the MMC is located to obtain the coupled state-space equation that takes MMC control into account. The coupled state-space equations are used to perform harmonic modeling of the converter station and the DC impedance matrix of the converter station is calculated.

2. The method according to claim 1, characterized in that The state space equation of establishing a single MMC includes: Establish the circuit equation of MMC based on the voltage-current relationship of MMC; The state space equation of MMC is established according to the circuit equation of MMC.

3. The method according to claim 2, characterized in that The state space equation of the MMC is established according to the circuit equation of the MMC, including: According to the circuit equation of MMC, the state space equation of MMC in three-phase stationary coordinate system is established; The state space equation of MMC in the three-phase stationary coordinate system is linearized to obtain the state space equation of MMC in the positive and negative sequence coordinate system.

4. The method according to claim 1, wherein The modulation ratio of the MMC is calculated according to the circulating current suppression control strategy of the MMC, including: The circulating current suppression control transfer function is established according to the charge transfer characteristics of the circulating current flowing in the converter station; A modulation ratio expression of a single MMC is established in the pn coordinate system, and the circulating current suppression control transfer function is substituted into the modulation ratio expression of the single MMC in the pn coordinate system, so that the modulation ratio is calculated according to the circulating current suppression control transfer function.

5. The method according to claim 4, characterized in that Substituting the circulating current suppression control transfer function into the modulation ratio expression of a single MMC in the pn coordinate system, the modulation ratio is calculated according to the circulating current suppression control transfer function: The modulation ratio expression of a single MMC is as follows: ， in, represents the transfer function matrix of the circulating current suppression controller, v DC Indicates the DC side voltage, represents the linearized small signal form of the common-mode current, Represents the common mode current in the pn coordinate system Transfer function matrix The modulation ratio obtained is represents the transfer function of the PR controller, k ccp and k ccr are the proportional gain coefficient and the resonant gain coefficient, represents the damping ratio, represents the natural frequency, and s is the Laplace operator.

6. The method according to claim 1, characterized in that The modulation ratio of MMC is calculated based on the voltage and current dual closed-loop control strategy of MMC, including: Let the d-axis of the first converter station control the DC voltage, the d-axis of the second converter station control the active power, and the q-axis of all MMCs control the AC voltage. Determine the control transfer function of the phase-locked loop in the rotating coordinate system. Considering the current inner loop control and voltage outer loop control, the control transfer function of the phase-locked loop is substituted into the modulation ratio expression of a single MMC in the rotating coordinate system, so that the modulation ratio is calculated according to the voltage and current dual closed-loop control transfer function.

7. The method according to claim 1, characterized in that The method of using coupled state-space equations to perform harmonic modeling on the converter station and calculate the DC impedance matrix of the converter station includes: The Toeplitz matrix is ​​introduced to shift the input frequency to the preset output frequency, and the coupled state space equation of a single converter station is converted from the time domain to the frequency domain to obtain a harmonic state space model. The DC impedance matrix of the converter station is calculated based on the harmonic matrix of the harmonic state space model.

8. A device for modeling DC impedance of an MMC bipolar system, characterized in that: include: A first state space modeling module is used to establish a state space equation for a single MMC; The second state space modeling module is used to establish the state space equation of a single converter station based on the AC side circuit coupling relationship and the state space equation of a single MMC; The coupling modeling module is used to construct the circulating current suppression control strategy and voltage-current dual closed-loop control strategy for a single MMC. The modulation ratio of the MMC is calculated based on the circulating current suppression control strategy and the voltage-current dual closed-loop control strategy. The modulation ratio of the MMC is substituted into the state space equation of the converter station where the MMC is located to obtain the coupled state space equation considering MMC control. The DC impedance calculation module is used to perform harmonic modeling of the converter station using coupled state-space equations and calculate the DC impedance matrix of the converter station.

9. An electronic device, characterized in that: The device comprises a memory storing computer executable instructions and a processor, and when the computer executable instructions are executed by the processor, the device executes the MMC bipolar system DC impedance modeling method according to any one of claims 1 to 7.

10. A readable storage medium, characterized in that: A computer executable program is stored, and when the program is executed, the MMC bipolar system DC impedance modeling method according to any one of claims 1 to 7 can be implemented.

Images