A method for modeling direct current impedance of MMC bipolar system and related device

Abstract

The application discloses a kind of MMC bipolar system direct current impedance modeling method and related device, belong to electrical engineering field, the modeling method has integrated alternating current coupling, control strategy dynamics and multi-frequency harmonic interaction by state space equation, the harmonic state space modeling framework presented can accurately analyze the influence of harmonic on direct current impedance, provides theoretical basis for system resonance suppression under weak power grid scene, the influence of the coupling part on circuit equation and modulation ratio transfer function in the AC side of converter station in bipolar system is considered, the state space equation of entire converter station is obtained;Using the relationship between input variable and state variable in harmonic state space equation, finally the direct current impedance matrix of bipolar system converter station is extracted, the modeling method presented in the application considers the generation mechanism of coupling impedance, establishes accurate mathematical model to characterize high-voltage direct current transmission system, lays an important foundation for stability analysis of the direct current side of converter station.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of electrical engineering, and particularly relates to a DC impedance modeling method for a MMC bipolar system and a related device. BACKGROUND

[0002] With the rapid popularization of renewable energy and distributed generation technology, and the continuous expansion of high-voltage direct current (HVDC) interconnection scale, the structure and dynamic characteristics of power systems are undergoing significant changes. High-voltage direct current transmission systems based on modular multilevel converters (MMC) have been widely used in grid interconnection, and more such systems will be put into use in the future. High-voltage direct current transmission systems are a complex system with multiple ports, and any resonance of the alternating current port can be amplified by the MMC to the direct current side, resulting in resonance of the entire direct current grid. Therefore, stability analysis must be performed to ensure safe operation of the system. However, the MMC has complex characteristics, and its internal multiple harmonics result in multi-frequency responses. In order to accurately model these multi-frequency responses, a harmonic state space (HSS) modeling method is introduced to describe its characteristics.

[0003] A bipolar structure similar to traditional direct current transmission systems can improve the voltage level and transmission capacity of flexible direct current transmission systems. In this system, one pole of the converter station is composed of a complete converter, and the two converters are grounded through a ground electrode lead. This structure not only improves the reliability of the system, but also provides technical support for the connection of large-scale renewable energy. However, when the converter station is connected to the grid through impedance, the alternating current side voltage is determined by the currents of the two MMCs. The two MMCs have mutual coupling parts, which not only affect the expression of the circuit equation, but also affect the small signal derivation of the control part, and the DC impedance of the two MMCs has coupling terms. Therefore, a method for establishing a DC side output impedance model of a bipolar MMC system is needed to analyze the influence of the coupling impedance on the stability of the system. SUMMARY

[0004] Based on this, the present application aims to provide a DC impedance modeling method for a MMC bipolar system and a related device to solve the problem of coupling terms in the DC impedance matrix of the bipolar MMC system, which affects the stability of the system.

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

[0006] establishing a state space equation for a single MMC;

[0007] establishing a state space equation for a single converter station according to the coupling relationship of the alternating current side circuit and the state space equation of the single MMC;

[0008] The control strategy of the single MMC is constructed, 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 control of the MMC is obtained.

[0009] The coupled state space equation is used to model the converter station in the harmonic, and the direct current impedance matrix of the converter station is calculated.

[0010] Further, the state space equation of the single MMC comprises:

[0011] The circuit equation of the MMC is established according to the voltage-current relationship of the MMC;

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

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

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

[0015] The state space equation of the MMC in the positive and negative sequence coordinate system is obtained by linearizing the state space equation of the MMC in the three-phase stationary coordinate system.

[0016] Further, the control strategy of the single MMC is constructed, 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 control of the MMC is obtained, comprising:

[0017] The circulating current suppression control strategy and the voltage-current double closed loop control strategy of the MMC are constructed;

[0018] The modulation ratio of the MMC is calculated according to the circulating current suppression control strategy and the voltage-current double closed loop control strategy of the MMC;

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

[0020] Further, the modulation ratio of the MMC is calculated according to the circulating current suppression control strategy of the MMC, comprising:

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

[0022] The circulating current suppression control transfer function is substituted into the modulation ratio expression of the single MMC in the rotating coordinate system, so that the modulation ratio is calculated according to the circulating current suppression control transfer function.

[0023] Further, the modulation ratio of the MMC is calculated according to the voltage-current double closed loop control strategy of the MMC, comprising:

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

[0025] Considering current inner loop control and voltage outer loop control, the control transfer function of the phase-locked loop is substituted into a 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 double closed loop control transfer function.

[0026] Further, a harmonic modeling is performed on the converter station by using a coupled state space equation, and a DC impedance matrix of the converter station is calculated, including:

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

[0028] The DC impedance matrix of the converter station is calculated according to a harmonic matrix of the harmonic state space model.

[0029] In a second aspect, the present application provides a DC impedance modeling device for an MMC bipolar system, including:

[0030] A first state space modeling module is configured to establish a state space equation of a single MMC.

[0031] A second state space modeling module is configured to establish a state space equation of a single converter station according to a coupling relationship of an AC side circuit and the state space equation of the single MMC.

[0032] A coupling modeling module is configured to construct a control strategy of the single MMC, and introduce the control strategy of the MMC of the same converter station into the state space equation of the converter station where the MMC is located, to obtain a coupled state space equation considering the MMC control.

[0033] A DC impedance calculation module is configured to perform a harmonic modeling on the converter station by using the coupled state space equation, and calculate a DC impedance matrix of the converter station.

[0034] In a third aspect, the present application provides an electronic device including a memory storing computer executable instructions and a processor, when the computer executable instructions are executed by the processor, the device is caused to perform each step of the MMC bipolar system DC impedance modeling method provided in the first aspect.

[0035] In a fourth aspect, the present application provides a readable storage medium storing computer executable instructions, when the instructions are executed, each step of the MMC bipolar system DC impedance modeling method provided in the first aspect can be realized.

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

[0037] The present application proposes a DC impedance modeling method for MMC bipolar system, which comprehensively integrates AC circuit coupling, control strategy dynamics and multi-frequency harmonic interaction through state space equation, breaks through the limitations of traditional model simplification of internal complex dynamics of MMC, the proposed harmonic state space modeling framework can accurately analyze the influence of harmonics on DC impedance, and provides a theoretical basis for system resonance suppression in weak grid scenarios, the designed circulating current suppression strategy effectively suppresses the second harmonic component in circulating current, and improves 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 DC impedance matrix of the bipolar system converter station is finally extracted by using the relationship between the input variables and the state variables in the harmonic state space equation, the modeling method proposed in the present application considers the generation mechanism of coupled impedance, and an accurate mathematical model is established to characterize the high voltage direct current transmission system, which lays an important foundation for stability analysis of the DC side of the converter station. BRIEF DESCRIPTION OF DRAWINGS

[0038] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, brief introductions to the drawings needed to be used in the embodiments or prior art descriptions will be given below. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor on the basis of the provided drawings.

[0039] Figure 1 The MMC bipolar system structure block diagram provided for the embodiments of the present application is shown in the figure.

[0040] Figure 2 The MMC bipolar system DC impedance modeling method implementation flowchart provided for the embodiments of the present application is shown in the figure.

[0041] Figure 3 The MMC bipolar system DC impedance modeling device structure schematic diagram provided for the embodiments of the present application is shown in the figure.

[0042] Figure 4 The electronic device architecture diagram provided for the embodiments of the present application is shown in the figure. DETAILED DESCRIPTION

[0043] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some embodiments of the present application, not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0044] Referring to Figure 1 One embodiment of the present application proposes a bipolar MMC high-voltage direct-current transmission system, which comprises two converter stations, each of which includes two identical MMC converters, and the converter stations are connected through a 400km overhead transmission line.

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

[0046] and represent the three-phase voltage of the AC power grid and the grid connection point respectively, is the voltage of the DC side neutral point, 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 is , the three-phase current of the lower bridge arm is , the average capacitor voltage of the upper bridge arm sub-module is , the average capacitor voltage of the lower bridge arm sub-module 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 sub-modules with a capacitance of and an inductor with an inductance of , and a resistance of .

[0047] Referring to Figure 2 Taking the MMC bipolar system as an example, one embodiment of the present application proposes a DC impedance modeling method for an MMC bipolar system, which comprises the following steps: Figure 1 Step S210. Establish the state space equation of a single MMC.

[0048] For a three-phase MMC, the relationship between the bridge arm voltage and the equivalent capacitor, and the relationship between the equivalent capacitor voltage and the bridge arm current are considered:

[0049]

[0050] The three-phase common-mode current on the AC side that circulates within the MMC bridge arm and does not appear on the AC terminal

[0051] is expressed as:

[0052] The differential-mode current on the AC side

[0053] can be calculated as:

[0054] ​

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

[0056]

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

[0058]

[0059] In the formula, L mac is the equivalent inductance through which the common-mode current i gabc flows, and is (0.5L m + L t ), L t is the transformer inductance, and the matrix form of each electrical quantity is as follows:

[0060]

[0061] In order to more clearly reflect the coupling relationship between different harmonics, 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), and the state space equation of the single MMC in the pn coordinate system is as follows:

[0062]

[0063] Among them, v DC represents the DC side voltage, v gpn0 represents the AC side grid connection point voltage, v cupn0 represents the upper bridge arm voltage, v clpn0 represents the lower bridge arm voltage, i gpn0 represents the AC side current, i cpn0 represents the common-mode current, n upn0 represents the modulation ratio of the upper bridge arm, and n lpn0 represents the modulation ratio of the lower bridge arm. Here, each electrical quantity is defined in the pn coordinate system, so it is 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 flow path for the zero sequence current on the AC side of the MMC, and the voltage after linearization is , which forces the system AC side small signal current to have no zero sequence component. Similarly, the following electrical quantities are in the form of linearized small signal form. ​

[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 above-mentioned variables with subscript pn0 represent positive, negative and zero sequence components in the pn coordinate system, respectively, and , for example, the elements in the matrix representation thereof , , respectively represent positive, negative and zero sequence components of the modulation ratio, and the remaining variables are understood as explained, which will not be repeated here.

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

[0081]

[0082] After only considering the 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, the form of the state space equation thereof can be expressed as:

[0083]

[0084] wherein is the state variable of converter station 1, is the derivative of the state variable of converter station 1. Δn pn0s1 represents the change amount of the modulation ratio of the MMC bridge arm in converter station 1, Δv DCs1 represents the change amount of the DC side voltage of the MMC in converter station 1, A 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 (refer to the M matrix in the state space equation when modeling a single MMC as described above), and 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 respectively represented as Δx pn0s1 and Δx pn0s2 , and are expressed as:

[0086]

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

[0088] Step S230. Constructing the control strategy of single MMC, introducing the control strategy of MMC in the same converter station into the state space equation of the converter station where the MMC is located, to obtain the coupled state space equation considering the control of MMC.

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

[0090] Circulating current flows in the bridge arm and deeply affects the internal dynamic characteristics of MMC. For a single MMC, to achieve circulating current suppression, an exemplary specific implementation scheme based on a proportional-resonant (PR) controller is described below.

[0091] Circulating current is mainly composed of even harmonics, among which the second harmonic component occupies a dominant position and is a negative sequence current. The control strategy sets the reference value to zero to suppress the harmonic. The controller acts on the common-mode component of the upper and lower arm modulation functions of the phase leg, and superimposes the output with the same sign into the upper and lower arm modulation functions, to realize the circulating current suppression function.

[0092]

[0093] wherein, represents the transfer function matrix of the circulating current suppression controller, represents the common-mode current in the pn coordinate system passes through the transfer function matrix to obtain the modulation ratio change amount, represents the transfer function of the PR controller, k ccp and k ccr are proportional gain coefficient and resonant gain coefficient respectively, 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 synchronization is realized by using a phase-locked loop to track the q-axis voltage. In the embodiment of the application, the d-axis of MMC1 and MMC2 controls the direct current voltage, the d-axis of MMC3 and MMC4 adopts P ac control, and the q-axis of the four MMCs controls alternating current voltage.

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

[0096]

[0097] k pllp and k plli 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 and the system-side dq coordinate system determined by the phase-locked loop coincide. The presence of voltage disturbance will cause the angle extracted by the phase-locked loop to deviate, thereby affecting the transformation between the dq coordinate systems.

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

[0100]

[0101] In the dq coordinate system, the control is carried out by using the per-unit value, wherein G pll (s) represents the transfer function of the phase-locked loop, G plli (s), G pllv (s) and G plln (s) represent the transfer function matrix of the phase-locked loop on the current, voltage and modulation ratio in the dq coordinate system, respectively, N 1ds and N 1qs are the steady-state values of the modulation ratio in the dq coordinate system, I ds and I qs are the steady-state values of the current in the dq coordinate system, V ds and V qs are the steady-state values of the voltage in the dq coordinate system. Δn 1dc , Δn 1qc , Δi dc , Δi qc , Δv dc and Δv qc are small disturbance electrical quantities in the controller dq coordinate system, Δn 1d , Δn 1q , Δi d , Δi q , Δv d and Δv q are small disturbance electrical quantities in the system dq coordinate system.

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

[0103]

[0104] wherein 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, wherein k pi and k ii represent the proportional gain and the integral gain of the PI controller in the current inner loop, respectively.

[0105] When only the current inner loop is considered, the expression of the output modulation ratio variation in the system-side dq coordinate system is:

[0106]

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

[0108] The V ac control is used in the outer loop of q-axis of 4 MMCs, and the reference current and its linearized small signal form are expressed as:

[0109]

[0110]

[0111]

[0112] where Δv dqc is the small perturbation of voltage in dq coordinate system of the controller, G acPI (s) represents the transfer function of PI controller in the outer loop of q-axis voltage, and represent the proportional gain and integral gain of PI controller in the outer loop of q-axis voltage, respectively, is the given AC voltage reference value, G vLPF represents the transfer function of low-pass filter in the outer loop of voltage, T v is the time constant of low-pass filter, is the transfer function from to in the outer loop of q-axis voltage, and is written in the form of 2x2 matrix for convenience of calculation.

[0113] The V ac control is used in the outer loop of d-axis of MMC1 and MMC2 to control DC voltage , and the reference current and its linearized small signal form are expressed as:

[0114]

[0115]

[0116] where G dcPI (s) represents the transfer function of PI controller in the outer loop of d-axis voltage, and represent the proportional gain and integral gain of PI controller in the outer loop of d-axis voltage, respectively, is the given DC voltage reference value, and G dcPI(s) is written in the form of a 2x2 matrix.

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

[0118]

[0119] In the formula, Δi dq1 and Δv dq1 represent the small perturbation of the current and voltage in the dq coordinate system of the system side of the MMC1, G vdq1 , G idq1 and G vdc represent the transfer function matrix from Δi dq1 , Δv dq1 and Δv DC1 to Δn 1dq1 , respectively.

[0120] It can be seen that in the dq control system, the grid-connected point voltage of the converter station in the bipolar MMC system is also determined by the currents of the two MMCs, and the grid-connected point voltage variation of the converter stations 1 and 2 is expressed as follows: Figure 1

[0121]

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

[0123] It is considered that the modulation ratio of the converter MMC1 not only includes the AC side current of the MMC1 itself, but also includes the AC side current of the MMC2, and therefore the MMC1 modulation ratio variation is expressed as follows:

[0124]

[0125] In the formula, G idq1 and G idq2 are the transfer functions from the currents Δi dq1 and Δi dq2 of the MMC to Δn 1dq1 in the dq coordinate system, G vdc is the transfer function from Δv DC to Δn 1dq1 , and G idq1 and G idq2 are both 2x2 matrices, and the matrix elements thereof are defined as G nidd1 , G nidq1 , G niqd1 , G niqq1 ​, G nidd2 , G nidq2 , G niqd2 and G niqq2 , which is convenient for subsequent conversion to the pn coordinate system.

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

[0127] The outer ring of the d-axis of MMC3 and MMC4 adopts P ac control, whose reference current and the expression of its linearized small signal form are as follows:

[0128]

[0129] where G pacPI (s) represents the transfer function of the d-axis power outer ring PI controller, k ppac and k piac represent the proportional gain and integral gain of the d-axis power outer ring PI controller respectively, G pLPF (s) represents the transfer function of the low-pass filter of the power outer ring, 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 the linearized small signal form Δp ac are calculated as follows:

[0130]

[0131]

[0132] where i dc , i qc represent the current in the dq coordinate system of the controller, v dc and v qc are the voltages in the dq coordinate system of the controller. and are the transfer functions from and to in the d-axis power outer ring.

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

[0134]

[0135] where Δv dq3 represents the small disturbance of the voltage in the dq coordinate system of the system side of MMC3, G vdq3is the transfer function from Δv dq3 to Δn 1dq3 in dq coordinate system. G idq3 and G idq4 are the transfer functions from Δi dq3 and Δi dq4 to Δn 1dq3 in dq coordinate system, G idq3 and G idq4 are both 2x2 matrices, whose matrix elements are defined as G nidd3 , G nidq3 , G niqd3 , G niqq3 , G nidd4 , G nidq4 , G niqd4 and G niqq4 , respectively, for the convenience of the following conversion to pn coordinate system.

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

[0137] The above transfer functions are established in dq coordinate system, and the expressions of the transfer functions in pn coordinate system after conversion are as follows:

[0138]

[0139] where G dd , , and are the transfer functions in matrix G idq1 , G idq2 , G idq3 and G idq4 corresponding to the subscript positions, respectively, and G idq1 , G idq2 , G idq3 and G idq4 converted to pn coordinate system are represented as G ipn01 , G ipn02 , G ipn03 and G ipn04 , respectively.

[0140] The expressions of modulation ratio variation of MMC1 and MMC3 in pn coordinate system are as follows:

[0141]

[0142] where Δn 1pn01 and Δn 1pn03 , the first number 1 of subscript represents the modulation ratio under double closed-loop control, and the following number 01 and 03 represent MMC1 and MMC3, respectively, G ipn01 and G ipn02 are 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 expression of the modulation ratio variation Δn pn02 of MMC2 can be obtained as follows:

[0148]

[0149] where M 22 , M DC2 and M 21 represent the transfer functions from Δx pn02 , Δv DC2 and Δx pn01 to Δn pn02 , and Δv DC2 represents the DC voltage variation of MMC2.

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

[0151]

[0152] Similarly, the expression of the modulation ratio variation Δn pn03 of MMC3 is as follows:

[0153]

[0154]

[0155] where Δn upn03 and Δn upn03 represent the modulation ratio variations of the upper and lower bridge arms of MMC3, and also include the transfer functions G ccpn03 representing the circulating current suppression control and the transfer functions G ipn03 , G ipn04 representing the double closed-loop control, M 33 and M 34 represent the transfer functions from Δx pn03 and Δx pn04 to Δn pn03 , and Δx pn03 and Δx pn04 represent the state variables of MMC3 and MMC4, respectively.

[0156] Similarly, the expression of the modulation ratio variation Δn 4pn0 of MMC4 is as follows:

[0157]

[0158] where M 44 and M 43 represent the transfer functions from Δxpn04 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 matrix element superscript represents different harmonic components.

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

[0183]

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

[0185]

[0186] In the above formula, Z DC11s1 and Z DC22s1 are diagonal element impedances of the converter station 1, Z DC11s2 and Z DC22s2 are diagonal element impedances of the converter station 2. Z DC12s1 and Z DC21s1 are coupling impedances of the converter station 1 considering coupling, and Z DC12s2 and Z DC21s2 are coupling impedances of the converter station 2 considering coupling.

[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 grid strength.

[0188] The MMC bipolar system DC impedance modeling method is described in detail in the above disclosed embodiments, and the above disclosed method can be implemented by various forms of equipment, so the application also discloses a modeling device corresponding to the above method, and specific embodiments are given below for detailed description.

[0189] As shown in Figure 3 , one embodiment of the application provides an MMC bipolar system DC impedance modeling device, which comprises:

[0190] A first state space modeling module 302 is configured to establish a state space equation of a single MMC.

[0191] A second state space modeling module 304 is configured to establish a state space equation of a single converter station according to the AC side circuit coupling relationship and the state space equation of the single MMC.

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

[0193] a DC impedance calculation module 308, configured to perform harmonic modeling on the converter station by using the coupled state space equation, and calculate a DC impedance matrix of the converter station.

[0194] The device provided in the embodiments of the present application has the same implementation principles and technical effects as the foregoing method embodiments, and for brief description, the part not mentioned in the device embodiment part can be referred to the corresponding content in the foregoing method embodiments.

[0195] The method and related device mentioned in the foregoing embodiments are described with reference to the method flowchart and / or structural schematic diagram provided in the embodiments of the present application, and each flow and / or block in the method flowchart and / or structural schematic diagram and the combination of the flows and / or blocks in the flowchart and / or block diagram can be implemented by computer program instructions. The computer program instructions can be provided to the 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 a method implemented in the flow Figure 1 The device specified in one flow or multiple flows and / or structural schematic Figure 1 The device specified in one flow or multiple flows and / or structural schematic Figure 1 The device specified in one flow or multiple flows and / or structural schematic Figure 1 The device specified in one flow or multiple flows and / or structural schematic Figure 1 The device specified in one flow or multiple flows and / or structural schematic

[0196] The following embodiments take the computer device to which the method is applied as an example for description. It can be understood that the computer device can be any device with operation and processing functions, which can be but is not limited to a server or a personal notebook computer. In one of the embodiments, the computer device can be an application server, which can be a server for running an application program to be tested.

[0197] Referring to Figure 4 which shows a hardware structure block diagram of an electronic device, the electronic device is intended to represent various forms of digital computers, such as laptops, desktops, workstations, personal digital assistants, servers, blade servers, mainframes, and other appropriate computers. The electronic device can also represent various forms of mobile devices, such as personal digital processors, cellular telephones, smart phones, wearable devices, and other similar computing devices. The components shown here, their connections, and their functions, as described above, are meant to be examples only, and are not intended to limit the implementations of the present application described and / or claimed in this document.

[0198] As Figure 4 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 embodiments 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 complete the communication with each other through the communication bus 4;

[0200] The processor 1 can 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 application, etc.

[0201] The memory 3 can include a high-speed RAM memory, and can also include a non-volatile memory, such as at least one disk memory, etc.

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

[0203] The embodiments of the present application also provide a readable storage medium having a computer program stored thereon, and the computer program is executed by the processor to implement the various processing procedures of the MMC bipolar system DC impedance modeling method provided by the above embodiments and / or any possible implementation manner combined with the embodiments.

[0204] The above-described embodiments of the application have been described in connection with what are presently considered to be the most practical and preferred implementations, it will be apparent to those of ordinary skill in the art that numerous modifications, implementations, and equivalents can be made without parting from the spirit and scope of the application. The specific naming of the components, capitalization of terms, the attributes, data structures, or any other programming or structural aspect is not mandatory or significant, and the mechanisms that implement the application or its features can have different names, formats, or protocols. The illustrated embodiments are described in enough detail to enable those with ordinary skill in the art to practice the application. It will be apparent to those of ordinary skill in the art that numerous implementations can be made without departing from the scope of the application. It is intended to include all such modifications, enhancements, alternatives, permutations, and equivalents as can be included within the spirit and scope of the application. The following claims are in no way intended to limit the scope of the present application to the precise

[0205] Those skilled in the art will appreciate that the various steps of the methods disclosed above can be implemented by general purpose computing devices, which can be centralized on a single computing device or distributed across a network of multiple computing devices, and optionally implemented in program code executable by a computing device, which can be stored in a storage device and executed by a computing device, or alternatively implemented as individual integrated circuit modules, or multiple modules or steps implemented as a single integrated circuit module. Thus, the embodiments of the present application are not limited to any particular combination of hardware and software.

[0206] The computing device executable program (also referred to as a program, software, software applications, or code) includes machine instructions for a programmable processor, and can be implemented using a high-level procedural and / or object-oriented programming language, and / or assembly / machine language. As used herein, the terms "machine-readable medium" and "computer-readable medium" refer to any computer program product, apparatus and / or device (e.g., magnetic discs, optical disks, memory, Programmable Logic Devices (PLDs)) used to provide 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 used to provide machine instructions and / or data to a programmable processor.

[0207] Certain aspects of the application include process steps and instructions described herein in the form of an algorithm. It should be noted that the process steps and instructions of the application can be embodied within software, firmware and / or hardware, and when implemented in software, they can be downloaded to be resident on and operated from different platforms used by a variety of operating systems.

[0208] Those skilled in the art can understand that the structure shown in each figure is only a block diagram of part of the structure related to the scheme of the present application, and does not constitute a limitation on the terminal device to which the scheme of the present application is applied. The specific terminal device can include more or fewer components than those shown in the figure, or combine certain components, or have a different arrangement of components.

[0209] In the description of the present specification, the description of the terms "one embodiment", "some embodiments", "an example", "a specific example", or "a possible design" and the like means that the specific features, structures, materials or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present application. In the present specification, the illustrative description of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any suitable manner in any one or more embodiments or examples. In addition, the person skilled in the art can combine and combine the different embodiments or examples described in the present specification and the features of the different embodiments or examples without contradiction.

[0210] Finally, it should also be noted that, in this document, the relationship terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between the entities or operations. Moreover, the terms "include", "contain" or any other variant thereof are intended to cover non-exclusive inclusion, so that the process, method, article or device including a series of elements not only includes those elements, but also includes other elements not explicitly listed or inherent to such process, method, article or device. Without more limitation, the element defined by the statement "including a" does not exclude the presence of additional identical elements in the process, method, article or device including the element.

[0211] The above embodiments are only used to illustrate the technical solutions of the present application, but not limited to them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that the technical solutions recorded in the foregoing embodiments can be modified, or some technical features can be replaced by equivalent; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

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 calculation of the modulation ratio of the MMC according to the circulating current suppression control strategy and the voltage-current dual closed-loop control strategy of the MMC includes: 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. 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. The modulation ratio expression of the single MMC is then expressed 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. The converter station is harmonic modeled using the coupled state-space equations, 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 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.

5. The method according to claim 1, wherein 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.

6. 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. When the coupling modeling module calculates the modulation ratio of the MMC according to the circulating current suppression control strategy and the voltage-current dual closed-loop control strategy of the MMC, the following process is specifically performed: 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. 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. The modulation ratio expression of the single MMC is then expressed 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, s is the Laplace operator; 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.

7. 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 5.

8. 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 5 can be implemented.

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