Method and device for establishing a wideband three-port frequency coupling impedance model of an MMC

Abstract

The application relates to the technical field of power system modeling and analysis, in particular to a method and device for establishing an MMC wide-frequency three-port frequency coupling impedance model, wherein the method comprises the following steps: a three-dimensional transfer function matrix of an MMC internal control link is established to determine a reference voltage generated by the MMC internal control link; based on the reference voltage and disturbance components of AC and DC sides of the MMC, dynamic quadratic iteration solving of MMC internal bridge arms is carried out to obtain actual output voltages of upper and lower bridge arms of the MMC; the actual output voltages of the upper and lower bridge arms are used to calculate a differential mode voltage and a common mode voltage of the MMC; and a wide-frequency three-port frequency coupling impedance model of the MMC for outputting stability of wide-frequency oscillation of a flexible AC / DC transmission system is established by using a differential mode voltage loop and a common mode voltage loop. Therefore, the problems that the impedance model established in the related art has a narrow applicable frequency range and low precision and cannot meet the requirements of wide-frequency oscillation stability analysis are solved.

Description

Technical Field

[0001] The present application relates to the technical field of power system modeling and analysis, and in particular to a method and device for establishing a broadband three-port frequency-coupled impedance model of an MMC (modular multilevel converter). Background Art

[0002] In recent years, many new types of power system broadband oscillation events have occurred in MMC-based flexible direct current transmission systems. In order to explore the mechanism of broadband oscillation of flexible direct current systems, it is urgent to establish an impedance model that can be used for broadband oscillation stability analysis of flexible direct current systems. The difficulty of flexible direct current system impedance modeling lies in the modeling of modular multilevel converters.

[0003] An MMC is composed of a cascade of multiple identical submodules. Compared to traditional two-level or three-level converters, MMCs have their own unique characteristics. First, MMCs are often used in high-voltage, high-capacity scenarios. Compared to two-level converters used in low-voltage, low-capacity scenarios, their control delay is often longer. Second, MMCs have unique internal bridge arm submodule dynamics, and their internal circulating current and circulating current suppression control have a significant impact on their impedance characteristics. The internal bridge arm dynamics of MMCs primarily affect the impedance characteristics in the low-frequency range, while their control and modulation delays primarily affect the high-frequency range of the MMC impedance characteristics.

[0004] However, the impedance modeling of MMC in related technologies mostly follows the modeling method of traditional two-level converters, without considering the influence of the MMC bridge arm dynamics and delay. The resulting impedance model has a narrow applicable frequency range and low accuracy, which cannot meet the requirements of broadband oscillation stability analysis. Summary of the Invention

[0005] The present application provides a method, apparatus, electronic device, and storage medium for establishing a broadband three-port frequency-coupled impedance model for MMC. This approach addresses the problem that in related technologies, impedance modeling for MMCs mostly follows the modeling method of traditional two-level converters, resulting in a narrow applicable frequency range and low accuracy for the established impedance model, which cannot meet the requirements for broadband oscillation stability analysis.

[0006] The first aspect of the present application provides a method for establishing an MMC broadband three-port frequency-coupled impedance model, comprising the following steps: establishing a three-dimensional transfer function matrix of an internal control link of the MMC, and determining a reference voltage generated by the internal control link of the MMC based on the three-dimensional transfer function matrix; performing a secondary iterative solution of the dynamics of the internal bridge arm of the MMC based on the reference voltage and the disturbance components of the AC side and the DC side of the MMC to obtain the actual output voltages of the upper bridge arm and the lower bridge arm of the MMC; calculating the differential-mode voltage and the common-mode voltage of the MMC according to the actual output voltages of the upper bridge arm and the lower bridge arm of the MMC, establishing a differential-mode voltage loop and a common-mode voltage loop based on the differential-mode voltage and the common-mode voltage respectively, and using the differential-mode voltage loop and the common-mode voltage loop to establish a broadband three-port frequency-coupled impedance model of the MMC for outputting the stability of the broadband oscillation of the flexible direct current system.

[0007] Furthermore, the broadband three-port frequency-coupled impedance model is:

[0008]

[0009] Where Z represents the three-port frequency-coupled impedance matrix, Z11, Z22, and Z33 are self-impedances, representing the impedance at the two coupled frequencies on the AC side and the impedance at the DC harmonic frequency, respectively; the remaining matrix elements are mutual impedances, representing the impedance between different frequencies on the AC side or between AC and DC; Vp and Vp2 represent the harmonic voltage components of the two frequency couplings on the AC side, respectively, and ΔVdc represents the harmonic voltage components on the DC side; Ip and Ip2 represent the harmonic current components of the two frequency couplings on the AC side, respectively, and ΔIdc represents the harmonic current components on the DC side; frequency coupling means that the sum of the frequencies of the two harmonic voltage or harmonic current components is twice the power frequency, that is, fp+fp2=2f1, where f1 is the frequency of the fundamental component, and * indicates taking the conjugate.

[0010] Furthermore, the establishment of the three-dimensional transfer function matrix of the MMC internal control link includes: obtaining the phase-locked loop dynamics, outer loop control dynamics, positive sequence current inner loop control dynamics, and negative sequence current inner loop control dynamics in the control link; and establishing the three-dimensional transfer function matrix according to the phase-locked loop dynamics, outer loop control dynamics, positive sequence current inner loop control dynamics, and negative sequence current inner loop control dynamics.

[0011] Furthermore, the secondary iterative solution of the MMC internal bridge arm dynamics based on the reference voltage and the disturbance components on the AC side and the DC side of the MMC to obtain the actual output voltages of the upper bridge arm and the lower bridge arm of the MMC includes: performing a first iterative solution based on the reference voltage and the disturbance components on the AC side and the DC side of the MMC to obtain the harmonic circulating current components; and performing a second iterative solution of the bridge arm dynamics based on the harmonic circulating current components to generate the actual output voltages of the upper bridge arm and the lower bridge arm of the MMC.

[0012] Furthermore, before performing a secondary iterative solution of the MMC internal bridge arm dynamics based on the reference voltage and the disturbance components on the AC side and the DC side of the MMC, it also includes: injecting a preset signal harmonic disturbance simultaneously on the AC side and the DC side of the MMC to generate the disturbance components on the AC side and the DC side of the MMC.

[0013] The second aspect of the present application provides an apparatus for establishing a broadband three-port frequency-coupled impedance model of an MMC, comprising: a derivation module for establishing a three-dimensional transfer function matrix of an internal control link of the MMC, and determining a reference voltage generated by the internal control link of the MMC based on the three-dimensional transfer function matrix; a solution module for performing a secondary iterative solution of the dynamics of the internal bridge arm of the MMC based on the reference voltage and the disturbance components of the AC side and the DC side of the MMC, to obtain the actual output voltages of the upper bridge arm and the lower bridge arm of the MMC; a modeling module for calculating the differential-mode voltage and the common-mode voltage of the MMC according to the actual output voltages of the upper bridge arm and the lower bridge arm of the MMC, establishing a differential-mode voltage loop and a common-mode voltage loop based on the differential-mode voltage and the common-mode voltage respectively, and using the differential-mode voltage loop and the common-mode voltage loop to establish a broadband three-port frequency-coupled impedance model of the MMC, and using the differential-mode voltage loop and the common-mode voltage loop to establish a broadband three-port frequency-coupled impedance model of the MMC for outputting the stability of broadband oscillation of a flexible direct current system.

[0014] Furthermore, the broadband three-port frequency-coupled impedance model is:

[0015]

[0016] Where Z represents the three-port frequency-coupled impedance matrix, Z11, Z22, and Z33 are self-impedances, representing the impedance at the two coupled frequencies on the AC side and the impedance at the DC harmonic frequency, respectively; the remaining matrix elements are mutual impedances, representing the impedance between different frequencies on the AC side or between AC and DC; Vp and Vp2 represent the harmonic voltage components of the two frequency couplings on the AC side, respectively, and ΔVdc represents the harmonic voltage components on the DC side; Ip and Ip2 represent the harmonic current components of the two frequency couplings on the AC side, respectively, and ΔIdc represents the harmonic current components on the DC side; frequency coupling means that the sum of the frequencies of the two harmonic voltage or harmonic current components is twice the power frequency, that is, fp+fp2=2f1, where f1 is the frequency of the fundamental component, and * indicates taking the conjugate.

[0017] Furthermore, the derivation module is further used to obtain the phase-locked loop dynamics, outer loop control dynamics, positive sequence current inner loop control dynamics, and negative sequence current inner loop control dynamics in the control link; and establish the three-dimensional transfer function matrix based on the phase-locked loop dynamics, outer loop control dynamics, positive sequence current inner loop control dynamics, and negative sequence current inner loop control dynamics.

[0018] Furthermore, the solution module is further used to perform a first iterative solution based on the reference voltage and the disturbance components on the AC side and the DC side of the MMC to obtain a harmonic circulating current component; and perform a second iterative solution of the bridge arm dynamics based on the harmonic circulating current component to generate the actual output voltages of the upper bridge arm and the lower bridge arm of the MMC.

[0019] Furthermore, it also includes: an injection module, which is used to inject a preset signal harmonic disturbance simultaneously on the AC side and DC side of the MMC before performing a secondary iterative solution of the MMC internal bridge arm dynamics based on the reference voltage and the disturbance components on the AC side and DC side of the MMC to generate the disturbance components on the AC side and DC side of the MMC.

[0020] The third aspect of the present application provides an electronic device, comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the method for establishing the MMC broadband three-port frequency-coupled impedance model as described in the above embodiment.

[0021] The fourth aspect of the present application provides a computer-readable storage medium having a computer program stored thereon, which is executed by a processor to implement the method for establishing the MMC broadband three-port frequency-coupled impedance model as described in the above embodiment.

[0022] Therefore, this application has at least the following beneficial effects:

[0023] After deducing the MMC control process, internal bridge arm dynamics, and external circuits, a broadband three-port frequency-coupled impedance model for the MMC was ultimately formed. By taking into account factors such as MMC control delay, signal transmission and calculation delays in the simulation software, and internal circulating currents and circulating current suppression control within the MMC, the resulting model ensures accuracy across a wide frequency range. The model also establishes the coupling relationship between the AC and DC sides of the converter, laying the foundation for stability analysis of flexible DC systems. This addresses the technical issue that prior MMC impedance modeling, which largely relies on the modeling methods of traditional two-level converters, results in a narrow applicable frequency range and low accuracy, making it incapable of meeting the requirements for broadband oscillation stability analysis.

[0024] Additional aspects and advantages of the present application will be given in part in the description below, and in part will become apparent from the description below, or will be learned through practice of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] The above and / or additional aspects and advantages of the present application will become apparent and easily understood from the following description of the embodiments in conjunction with the accompanying drawings, in which:

[0026] Figure 1 Flowchart of a method for establishing an MMC broadband three-port frequency-coupled impedance model according to an embodiment of the present application;

[0027] Figure 2 A diagram showing a single-phase topological structure of a modular multilevel converter according to an embodiment of the present application;

[0028] Figure 3 A flowchart of a method for establishing an MMC broadband three-port frequency-coupled impedance model according to one embodiment of the present application;

[0029] Figure 4 This is an example diagram of a device for establishing an MMC broadband three-port frequency-coupled impedance model according to an embodiment of the present application;

[0030] Figure 5 A schematic diagram of the structure of an electronic device provided according to an embodiment of the present application. DETAILED DESCRIPTION

[0031] The following describes in detail embodiments of the present application, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present application, and should not be construed as limiting the present application.

[0032] Broadband oscillations in flexible DC systems can occur in multiple scenarios. For example, when large-scale renewable energy stations are transmitting power via flexible DC, high-frequency oscillations can occur between the sending-side converter and the offshore wind farm. In back-to-back DC transmission, high-frequency oscillations can also occur between the inverter-side converter and the AC grid. Therefore, to analyze broadband oscillations in these scenarios, it is necessary to develop an impedance model that considers both the AC and DC port characteristics of the MMC. The MMC itself has both AC and DC ports, with different converters interconnected via the DC grid. However, current impedance modeling efforts typically separate the overall AC-DC-AC system, assuming either the DC or AC side remains constant. These impedance models only model the MMC impedance as viewed from the AC port, or only the DC port. These impedance models fail to account for the impact of the AC or DC system on their own impedance characteristics, limiting their application in addressing broadband oscillations in flexible DC systems across multiple scenarios. There is a lack of an impedance model that can simultaneously represent the characteristics of both the AC and DC ports of the MMC.

[0033] Limited by modeling methods and mathematical theories, MMCs in high-voltage, high-capacity scenarios have severely hampered stability research in the broadband oscillation domain of flexible DC systems. Therefore, this paper proposes a broadband three-port frequency-coupled impedance modeling method that accounts for the dynamics of the MMC's internal bridge arms. This three-port frequency-coupled impedance model constructs the coupling relationship between the AC and DC sides of the MMC. The proposed model has important theoretical and engineering implications for studying the broadband oscillation mechanisms of flexible DC transmission systems and improving the stability of flexible DC systems.

[0034] For the purpose of studying the stability of power systems, especially the stability analysis of broadband oscillations in flexible DC systems, the embodiments of the present application provide a broadband three-port frequency-coupled impedance modeling method, device, electronic device and storage medium that take into account the dynamics of the internal bridge arm of the MMC.

[0035] The following describes the method, device, electronic device and storage medium for establishing the MMC broadband three-port frequency-coupled impedance model of the embodiment of the present application with reference to the accompanying drawings. In view of the problem that the impedance modeling work of MMC in the related art mentioned in the above background technology mostly follows the modeling method of the traditional two-level converter, the established impedance model has a narrow applicable frequency range and low accuracy, and cannot meet the requirements of broadband oscillation stability analysis, the present application provides a method for establishing the MMC broadband three-port frequency-coupled impedance model. In this method, after the derivation of the MMC control link, the internal bridge arm dynamics and the external circuit, the broadband three-port frequency-coupled impedance model of the MMC is finally formed. Since all factors such as the MMC control delay, the transmission and calculation delay of the signal in the simulation software, and the internal circulating current and circulating current suppression control of the MMC are taken into account, the obtained model can ensure accuracy within a broadband range. At the same time, the model constructs the coupling relationship between the AC side and the DC side of the converter, laying the foundation for the stability analysis of the flexible direct current system. This solves the technical problems that the impedance modeling of MMC in related technologies mostly follows the modeling method of traditional two-level converters, the established impedance model has a narrow applicable frequency range and low accuracy, and cannot meet the requirements of wide-band oscillation stability analysis.

[0036] Specifically, Figure 1 A flow chart of a method for establishing an MMC broadband three-port frequency-coupled impedance model provided in an embodiment of the present application.

[0037] like Figure 1 As shown, the method for establishing the MMC broadband three-port frequency-coupled impedance model includes the following steps:

[0038] In step S101 , a three-dimensional transfer function matrix of an internal control link of the MMC is established, and a reference voltage generated by the internal control link of the MMC is determined based on the three-dimensional transfer function matrix.

[0039] In this embodiment, a three-dimensional transfer function matrix of the internal control link of the MMC is established, including: obtaining the phase-locked loop dynamics, outer loop control dynamics, positive sequence current inner loop control dynamics, and negative sequence current inner loop control dynamics in the control link; and establishing the three-dimensional transfer function matrix based on the phase-locked loop dynamics, outer loop control dynamics, positive sequence current inner loop control dynamics, and negative sequence current inner loop control dynamics.

[0040] It can be understood that the embodiment of the present application establishes a three-dimensional transfer function matrix of the MMC control link, taking into account control links such as Park transformation, phase-locked loop, various outer loop controls, positive sequence current inner loop control, negative sequence current inner loop control, and Park inverse transformation, and derives the reference voltage generated by the MMC internal control link, including the fundamental component and two frequency-coupled harmonic components.

[0041] In step S102 , a secondary iterative solution of the internal bridge arm dynamics of the MMC is performed based on the reference voltage and the disturbance components of the AC side and the DC side of the MMC to obtain the actual output voltages of the upper bridge arm and the lower bridge arm of the MMC.

[0042] It is understandable that the embodiments of the present application can dynamically derive the actual output voltage of the upper and lower bridge arms of the MMC based on the reference voltage, circulating current and current components on the AC and DC sides through the MMC bridge arms.

[0043] In this embodiment, a secondary iterative solution of the internal bridge arm dynamics of the MMC is performed based on the reference voltage and the disturbance components on the AC side and the DC side of the MMC to obtain the actual output voltages of the upper bridge arm and the lower bridge arm of the MMC, including: performing a first iterative solution based on the reference voltage and the disturbance components on the AC side and the DC side of the MMC to obtain the harmonic circulating current components; and performing a second iterative solution of the bridge arm dynamics based on the harmonic circulating current components to generate the actual output voltages of the upper bridge arm and the lower bridge arm of the MMC.

[0044] It can be understood that the embodiment of the present application can dynamically derive the harmonic circulating current component through the MMC bridge arm based on the reference voltage and AC and DC side harmonic disturbance components derived above; then, after considering the harmonic circulating current component, the second iteration of the bridge arm dynamics is performed to derive the upper and lower bridge arm voltages.

[0045] It should be noted that the circulating current suppression control is closely related to the internal dynamics of the bridge arm, and is solved in two cases depending on whether the circulating current suppression control is put into operation; when the circulating current suppression control is not considered, the bridge arm modulation wave does not contain the double frequency negative sequence circulating current component, but there is a double frequency negative sequence circulating current component; when the circulating current suppression control is considered, the double frequency negative sequence circulating current component is no longer considered, but the double frequency negative sequence circulating current component in the modulation wave must be considered.

[0046] Specifically, the single-phase topology of MMC is as follows: Figure 2 As shown, where j = A, B, C. Each bridge arm is composed of a bridge arm inductor L0, a bridge arm resistor R0 and N submodules connected in series. Figure 1 It can be seen that the bridge arm current will contain both the AC side current and the DC side current; however, in addition to this, the bridge arm current will also contain internal circulating currents caused by the inconsistency between the sums of the upper and lower bridge arm voltages of each phase. Therefore, the MMC bridge arm current can be expressed as:

[0047]

[0048] Among them, i Tj (t), i Bj (t) represents the upper and lower arm currents of a phase, i cirj (t) represents the circulation component of a phase, i' j(t) represents the valve-side current of a certain phase of the converter transformer.

[0049] Assuming the dynamic response of each bridge arm submodule in the MMC is consistent, the modulation wave of each bridge arm is the arithmetic mean of the switching functions of each submodule in that bridge arm. The modulation waves of the upper and lower bridge arms of the MMC are related to the reference voltage generated by the control link. Since the reference voltage is calculated by the previous control link, the bridge arm voltage calculation here should be one simulation step ahead to compensate for the calculation delay of the previous control link. It can be expressed as:

[0050]

[0051] Among them, m Tj (t), m Bj (t) are the modulation waves of the upper and lower bridge arms of a phase of the converter, Indicates the reference voltage generated by the MMC control link, T d Indicates the simulation step size of the electromagnetic transient simulation software.

[0052] The same electrical quantity in the upper and lower bridge arms of each phase of the MMC is symmetrical, and they differ from each other in the time domain by T / 2, where T represents the fundamental wave period. Therefore, the same electrical quantity in the lower bridge arm can be directly obtained from the electrical quantity in the upper bridge arm. In addition, the same electrical quantity in the three phases of the MMC will lag behind by T / 3 in the time domain. Therefore, the dynamics of all six bridge arms can be derived based on the dynamics of a certain bridge arm. Taking the upper bridge arm of phase A as an example, since the modulation wave of each bridge arm is the arithmetic mean of the switching functions of each sub-module in the bridge arm, the arithmetic mean of the sub-module capacitor current can be directly calculated from the bridge arm modulation wave and the bridge arm current, which can be expressed as:

[0053]

[0054] in, Indicates the capacitance current of the upper bridge arm submodule of phase a, i Ta (t) represents the upper arm current of phase A, m Ta (t) represents the modulation wave of the upper arm of phase A.

[0055] Under steady-state operation, the DC component of the submodule capacitor current should be zero, otherwise the capacitor voltage will continue to increase. Therefore, the DC component of the submodule capacitor current in Equation 3 should be ignored before being substituted into subsequent calculations. Based on the capacitance of the submodule capacitor and the arithmetic mean of the submodule capacitor current, the arithmetic mean of the submodule capacitor voltage can be further calculated and expressed as:

[0056]

[0057] in, It represents the capacitor voltage of the upper bridge arm submodule of phase A, and C0 represents the DC capacitance of the submodule.

[0058] The submodule capacitor voltage is coupled to the bridge arm through the submodule switching action. Therefore, the bridge arm voltage can be calculated from the average value of the submodule capacitor voltage and the bridge arm modulation wave. Considering the internal calculation delay of the simulation software, the submodule capacitor voltage calculated by the above formula needs to be delayed by one simulation step before being brought into the calculation. The bridge arm voltage of phase A of the MMC can be obtained as:

[0059]

[0060] Among them, u Ta (t) is the bridge arm voltage of phase A, and N is the number of bridge arm submodules.

[0061] Since the same electrical quantity of the upper and lower bridge arms of each phase is symmetrical, the same-phase lower bridge arm voltage u can be directly obtained from the upper bridge arm voltage Ba (t). Taking into account the internal calculation delay of the simulation software, the bridge arm voltage calculated above also needs to be delayed by one simulation step to obtain the accurate bridge arm voltage. The arithmetic mean of the above-corrected upper and lower bridge arm voltages can be obtained to obtain the common mode voltage of the MMC:

[0062]

[0063] Among them, u coma (t) is the common-mode voltage of phase A.

[0064] The injection of harmonic disturbance components from the AC and DC sides will generate new harmonic components in the circulating current within the MMC. Therefore, the bridge arm voltage and common-mode voltage should be determined in the first iteration according to the above steps. The harmonic circulating current components should then be solved based on the common-mode voltage loop. Subsequently, the circulating current and reference voltage should be corrected, and the bridge arm voltage should be solved in a second iteration. After two iterations, relatively accurate upper and lower arm voltages can be obtained.

[0065] In this embodiment, before performing a secondary iterative solution of the MMC internal bridge arm dynamics based on the reference voltage and the disturbance components on the AC side and DC side of the MMC, it also includes: injecting a preset signal harmonic disturbance simultaneously on the AC side and DC side of the MMC to generate disturbance components on the AC side and DC side of the MMC.

[0066] Specifically, the embodiment of the present application derives the three-port frequency-coupled impedance based on the multi-harmonic linearization modeling method. The harmonic linearization method is to add a small-signal harmonic disturbance to the steady-state operating point of the target object, and then extract the harmonic signal at the corresponding frequency in its response, and then obtain the equivalent impedance of the target object. In order to establish a three-port frequency-coupled impedance model that can uniformly represent the AC and DC dynamic characteristics of MMC, it is necessary to inject small-signal harmonic disturbances into the AC and DC sides of the MMC at the same time. MMC has a frequency coupling effect due to the coordinate transformation and phase-locked loop dynamics in its internal control. Therefore, it is necessary to add two frequency-coupled harmonic disturbances to the steady-state power frequency voltage signal on the AC side of the MMC at the same time. The A-phase grid voltage after adding the small-signal harmonic disturbance can be expressed as follows:

[0067] u a (t)=V1 cos(ω1t)+V p cos(ω p t+φ p )+V p2 cos(ω p2 t+φ p2 ) (7)

[0068] Where V1 is the amplitude of the fundamental voltage, ω1 is the angular frequency of the fundamental voltage, ω1 = 2πf1, f1 is the frequency of the fundamental voltage; V p is the amplitude of the harmonic voltage, ω p is the angular frequency of the harmonic voltage, ω p =2πf p , f p is the frequency of the harmonic voltage, φ p is the initial phase angle of the harmonic voltage; V p2 is the amplitude of the harmonic voltage at the coupling frequency, ω p2 is the angular frequency of the harmonic voltage at the coupling frequency, ω p2 =2πf p2 , f p2 is the frequency of the harmonic voltage at the coupling frequency, φ p2 is the initial phase angle of the harmonic voltage at the coupling frequency.

[0069] After adding two frequency-coupled harmonic disturbances to the steady-state power frequency voltage signal on the AC side of the MMC, the A-phase grid current can be expressed as follows:

[0070]

[0071] Where I1 is the amplitude of the fundamental current, is the initial phase angle of the fundamental current; I p is the amplitude of the harmonic current, is the initial phase angle of the harmonic current; I p2 is the amplitude of the harmonic current at the coupling frequency, is the initial phase angle of the harmonic current at the coupling frequency.

[0072] It should be noted that since the injected harmonic disturbance component is an AC signal, the phase angles of the positive-sequence and negative-sequence components of the AC signal have different representations. To simplify the derivation process, the embodiments of the present application can represent all AC signals in the form of the phase angle of the positive-sequence component, and use the positive and negative frequencies to distinguish between the positive and negative sequence components, eliminating the need to distinguish between the positive and negative sequence components and represent them separately.

[0073] In addition, to represent the DC dynamics of the MMC, an additional harmonic disturbance is added to the steady-state DC voltage signal on the DC side of the MMC. The frequency of the small-signal harmonic disturbance on the DC side is related to the frequency of the harmonic disturbance injected on the AC side. According to the instantaneous power formula, the active power output of the MMC can be expressed as:

[0074] P=u a (t)i a (t)+u b (t)i b (t)+u c (t)i c (t) (9)

[0075] After considering the two frequency coupled harmonic disturbances injected into the AC side of the MMC, the active power of the MMC will contain a harmonic disturbance with a frequency of f p -f1 harmonic components. According to the active power conservation law, we can get:

[0076] P=u dc (t)i dc (t) (10)

[0077] Among them, u dc Indicates DC voltage, i dc Indicates direct current.

[0078] From the above formula, we can see that after considering the harmonic disturbance injected into the AC side of the MMC, a frequency of f will be generated in the DC voltage and DC current. p -f1 harmonic component. Therefore, the frequency of the DC side small signal harmonic disturbance is f p -f1, which is convenient for the subsequent derivation of the DC dynamics of the MMC. The DC voltage after adding the small signal harmonic disturbance can be expressed as follows:

[0079] u dc (t) = V dc0 +ΔV dc cos[(ω p -ω1)t+φ dc ] (11)

[0080] Among them, V dc0is the amplitude of the DC steady-state voltage, ΔV dc is the amplitude of the DC side harmonic voltage, φ dc Based on the three harmonic disturbances injected into the AC and DC sides, the present embodiment establishes an MMC broadband three-port frequency-coupled impedance model.

[0081] In step S103, the differential-mode voltage and common-mode voltage of the MMC are calculated according to the actual output voltages of the upper bridge arm and the lower bridge arm of the MMC, and a differential-mode voltage loop and a common-mode voltage loop are established based on the differential-mode voltage and the common-mode voltage, respectively. The differential-mode voltage loop and the common-mode voltage loop are used to establish a wide-band three-port frequency-coupled impedance model of the MMC for outputting the stability of the wide-band oscillation of the flexible direct current system.

[0082] It can be understood that the embodiment of the present application can calculate the differential-mode voltage and common-mode voltage of the MMC by deriving the upper and lower bridge arm voltages, and use the differential-mode voltage loop and common-mode voltage loop of the MMC to establish the relationship between the MMC and the external circuit to obtain a broadband three-port frequency-coupled impedance model of the MMC.

[0083] Specifically, the bridge arm voltage can be further calculated to obtain the differential-mode voltage and common-mode voltage of the MMC. The differential-mode voltage is actually the output voltage on the AC side of the MMC. The relationship between the differential-mode loop and the electrical quantities on both sides of the converter transformer can be used to establish an expression for the harmonics injected from the AC side. The common-mode voltage can be combined with the common-mode loop to establish an expression for the harmonics injected from the DC side. Furthermore, a broadband three-port frequency-coupled impedance model of the MMC can be established. The three-port frequency-coupled impedance model: a three-dimensional matrix containing self-impedance and mutual impedance, can be expressed as:

[0084]

[0085] Where Z represents the three-port frequency-coupled impedance matrix, Z11, Z22, and Z33 are self-impedances, representing the impedance at the two coupled frequencies on the AC side and the impedance at the DC harmonic frequency, respectively; the remaining matrix elements are mutual impedances, representing the impedance between different frequencies on the AC side or between AC and DC; Vp and Vp2 represent the harmonic voltage components of the two frequency couplings on the AC side, respectively, and ΔVdc represents the harmonic voltage components on the DC side; Ip and Ip2 represent the harmonic current components of the two frequency couplings on the AC side, respectively, and ΔIdc represents the harmonic current components on the DC side; frequency coupling means that the sum of the frequencies of the two harmonic voltage or harmonic current components is twice the power frequency, that is, fp+fp2=2f1, where f1 is the frequency of the fundamental component, and * indicates taking the conjugate.

[0086] The following will describe the method for establishing the MMC broadband three-port frequency coupled impedance model through a specific embodiment. Figure 3As shown, comprising the following steps:

[0087] Step 1: Derive the phase-locked loop dynamics in the control loop to obtain the frequency domain expression of the harmonic components in the phase angle of the phase-locked loop output.

[0088] Step 2: Derive the outer loop control dynamics

[0089] The outer loop control includes active control, reactive control, DC voltage control, AC voltage control, etc. The derivation methods of the above different controls are basically the same, and finally generate the reference currents of the d-axis and the q-axis.

[0090] The embodiments of the present application give the transfer function matrix of the outer loop control in the form of a modular matrix. When different control schemes are adopted, the transfer function matrix can be replaced, and the entire control loop does not need to be re-derived.

[0091] Step 3: Derive the positive sequence current inner loop control dynamics

[0092] The positive sequence current inner loop control can use the transformer network side current as the input quantity, or use the transformer valve side current as the input quantity. After considering the Park transformation and the positive sequence current inner loop PI control, the DC component and the harmonic component with a frequency of f p -f1 will be included in the dq-axis voltage reference value.

[0093] Further, after the Park inverse transformation, the three-phase voltage reference value obtained finally will contain harmonic components with frequencies of f p and 2f1-f p . In order to unify the form of harmonic voltage disturbance, the conjugate of the formula under the coupling frequency is taken.

[0094] Step 4: Derive the negative sequence current inner loop control dynamics

[0095] The phase angle used by the Park transformation in the negative sequence current inner loop control is obtained by taking the opposite of the phase angle of the Park transformation in the positive sequence current inner loop. After considering the Park transformation and the negative sequence current inner loop PI control, the dq-axis voltage reference value will include the double frequency component and the harmonic components with frequencies of f p +f1 and f p -3f1. Among them, the double frequency component is generated by the positive sequence fundamental component. In order to avoid the influence of the positive sequence fundamental component on the negative sequence current inner loop control, a positive sequence fundamental component elimination link is added after the Park transformation.

[0096] Further, after the Park inverse transformation, the three-phase voltage reference value obtained finally will contain harmonic components with frequencies of f p , 2f1-f p , -f p -2f1 and f p-4f1 harmonic components. Since the PI parameters used for the current inner loop dq axis control are generally the same after the voltage and current are normalized, the following relationship can be established between the dq axis voltage reference values ​​of different frequency components:

[0097]

[0098] in, Indicates the d-axis voltage reference value generated by the negative sequence current inner loop, Represents the q-axis voltage reference value generated by the negative sequence current inner loop.

[0099] After substituting equation (12), the frequency of the three-phase voltage reference value is f p -4f1 and -f p The harmonic components of -2f1 are all zero. Therefore, the negative sequence current inner loop control finally only outputs the frequency f p and 2f1-f p In order to unify the form of harmonic voltage disturbance, the formula at the coupling frequency is conjugated.

[0100] Step 5: Converter transformer broadband modeling

[0101] The positive- and negative-sequence current inner-loop control uses the transformer valve-side current as input. The d / q axis current components derived from the Park transform are related to the valve-side harmonic disturbance. Therefore, it is necessary to derive the relationship between the transformer valve-side electrical quantities and the grid-side electrical quantities.

[0102] After accounting for the magnetizing reactance, the relationship between the converter transformer valve-side voltage and current and the grid-side voltage and current phasors at the harmonic and coupling frequencies can be expressed as follows. To unify the representation of harmonic voltages and currents, the formulas at the coupling frequency are conjugated.

[0103]

[0104]

[0105] Among them, V' p and V' p2 Represents the two frequency coupled harmonic voltage components on the transformer valve side, I' p and I' p2 They represent the two frequency coupled harmonic current components on the transformer valve side.

[0106] Step 6: Derive the overall transfer function of the control link

[0107] According to the derivation results of steps 2, 3, and 5, the phase A voltage reference value generated by the positive sequence current inner loop control can be expressed as:

[0108]

[0109] in, Indicates the phase A voltage reference value generated by the positive sequence current inner loop control.

[0110] According to the derivation results of steps 4 and 5, the phase A voltage reference value generated by the negative sequence current inner loop control is:

[0111]

[0112] in, Indicates the phase A voltage reference value generated by the negative-sequence current inner loop control.

[0113] The voltage reference values ​​generated by the positive-sequence and negative-sequence current inner loop control are superimposed and passed through a modulation ratio link to obtain the total reference voltage generated by the control link. After considering the modulation ratio and controller delay link, the harmonic components in the total reference voltage can be expressed as:

[0114]

[0115] in, Represents the total reference voltage generated by the control link at the two coupling frequencies.

[0116] Step 7: Derivation of the double frequency negative sequence circulating current inside the MMC

[0117] In the steady state, in addition to the fundamental component on the AC side and the DC component on the DC side, there is also a double frequency negative sequence circulating current in the bridge arm of the MMC. In order to avoid the increase of model complexity, the present invention dynamically derives the double frequency negative sequence circulating current component I through the bridge arm. cir , the circulating current is represented by known electrical quantities and component parameters, avoiding the introduction of new variables and reducing the complexity of the model.

[0118] Step 8: Dynamic Derivation of MMC Bridge Arm

[0119] Based on the reference voltage derived in step 6, the doubled-frequency negative-sequence circulating current derived in step 7, and the harmonic disturbance components on the AC and DC sides, the MMC arm output voltage after harmonic injection can be derived through the MMC arm dynamics. However, the harmonic disturbance components injected on the AC and DC sides will cause new harmonic components to appear in the MMC's internal circulating current, so a two-iteration method is required to solve the arm dynamics; the first iteration determines the components of the harmonic circulating current, and the second iteration completes the solution for the harmonic circulating current and arm voltage. In addition, because the arm dynamics involve internal circulating currents, the solution must be divided into two cases depending on whether the circulating current suppression control is in operation.

[0120] (1) Circulation suppression control is not put into operation

[0121] 1) First Iteration

[0122] The single-phase topology of MMC Figure 1 It can be seen that the bridge arm current includes the AC side current, DC side current and internal circulating current. Therefore, the bridge arm current of the MMC can be expressed as:

[0123]

[0124] When the circulation suppression control is not in operation, i cira (t) contains only the double frequency negative sequence circulating current component, i' a (t) includes the fundamental component and the frequency f p and 2f1-f p The two coupled harmonic components of dc (t) contains a DC component and a frequency of f p - Harmonic components of f1.

[0125] The modulation wave of the upper bridge arm of the MMC is related to the reference voltage generated by the control link. When the circulating current suppression control is not in operation, it includes the fundamental component and two frequency-coupled harmonic components. Since the reference voltage is calculated by the preceding control link, the calculation of the bridge arm voltage here should be advanced by one simulation step to compensate for the calculation delay of the preceding control link. It can be expressed as:

[0126]

[0127] in, Including the fundamental component and two frequency coupled harmonic components, V1 pu-r 、 and are the amplitudes of the fundamental component and the two frequency-coupled harmonic components in the reference voltage, and are the initial phase angles of the fundamental component and the two harmonic components respectively.

[0128] Since the modulation wave of each bridge arm is the arithmetic mean of the switching functions of each sub-module in the bridge arm, the arithmetic mean of the sub-module capacitor current can be directly calculated from the bridge arm modulation wave and the bridge arm current, which can be expressed as:

[0129]

[0130] Furthermore, after ignoring the DC component in the submodule capacitor current, the arithmetic mean of the submodule capacitor voltage can be further calculated based on the capacitance of the submodule capacitor and the arithmetic mean of the submodule capacitor current, which can be expressed as:

[0131]

[0132] Taking into account the internal calculation delay of the simulation software, the submodule capacitor voltage calculated by the above formula needs to be delayed by one simulation step before being brought into the calculation. The voltage of the upper bridge arm of phase A of the MMC can be obtained as follows:

[0133]

[0134] Since the same electrical quantity of the upper and lower bridge arms of each phase of the MMC is symmetrical, the voltage u of the lower bridge arm in the same phase can be directly obtained from the voltage of the upper bridge arm. Ba Taking into account the internal calculation delay of the simulation software, the bridge arm voltage calculated above needs to be delayed by one simulation step to obtain the accurate bridge arm voltage.

[0135]

[0136] According to the expanded result of formula 23, after considering the harmonic disturbance injected from the AC side and the DC side, the common mode voltage of the MMC will couple a frequency of -f p -f1,f p -3f1,f p +3f1 and 5f1-f p However, the DC side of the MMC only contains DC components and harmonic components with a frequency of f p The harmonic disturbance component of -f1, combined with the common-mode circuit, shows that the harmonic components in the common-mode voltage will generate harmonic components of the same frequency in the internal circulating current of the MMC. When the circulating current suppression control is not activated, the bridge arm modulation wave remains unchanged, and the internal circulating current of the MMC can be rewritten as:

[0137]

[0138] Among them, I cir represents the amplitude of the double frequency negative sequence circulating current component, φ cir Indicates the initial phase angle of the double frequency negative sequence circulating current component; I cir2 Indicates frequency as -f p -f1 harmonic circulating current component amplitude, φ cir2 Indicates frequency as -f p -f1 initial phase angle of harmonic circulating current component; I cir3 Indicates frequency f p -3f1 harmonic circulating current component amplitude, φ cir3 Indicates frequency f p -3f1 initial phase angle of harmonic circulating current component; I cir4 Indicates frequency f p The amplitude of the +3f1 harmonic circulating current component, φ cir4 Indicates frequency f p +3f1 initial phase angle of harmonic circulating current component; I cir5 Indicates the frequency is 5f1-f pAmplitude of the harmonic circulating current component, φ cir5 Indicates the frequency of 5f1-f p Initial phase angle of the harmonic circulating current component.

[0139] 2) Second iteration

[0140] According to the foregoing derivation, the internal circulating current of MMC includes harmonic components of frequency -f p -f1, f p -3f1, f p +3f1and 5f1-f p in addition to the double-frequency negative sequence component. Therefore, the bridge arm dynamics need to be iterated twice after the circulating current is corrected.

[0141] The arithmetic mean of the submodule capacitor current can be calculated from the corrected bridge arm current and the bridge arm modulation wave:

[0142]

[0143] After ignoring the DC component in the submodule capacitor current, the arithmetic mean of the submodule capacitor voltage can be obtained:

[0144]

[0145] Considering the internal calculation delay of the simulation software, the submodule capacitor voltage calculated by the above formula is delayed by one simulation step before being brought into the calculation, and the upper bridge arm voltage of phase A of the MMC is obtained:

[0146]

[0147] Since the same kind of electrical quantity of the upper and lower bridge arms of each phase is symmetrical, the lower bridge arm voltage u Ba (t) of the same phase can be directly obtained from the upper bridge arm voltage. Considering the internal calculation delay of the simulation software, the bridge arm voltage obtained by the above calculation also needs to be delayed by one simulation step before the accurate bridge arm voltage is obtained.

[0148] (2) Circulating current suppression control operation

[0149] 1) First iteration

[0150] In the case of circulating current suppression control operation, the double-frequency negative sequence circulating current no longer exists, and the reference voltage generated by the control link will additionally include the double-frequency negative sequence component generated by the circulating current control. Since the reference voltage is calculated by the previous control link, it should be advanced by one simulation step when calculating the bridge arm voltage to compensate for the calculation delay of the previous control link, which can be represented as:

[0151]

[0152] wherein, Including fundamental component, double frequency negative sequence component and two frequency coupled harmonic components, V cir Indicates the amplitude of the double frequency negative sequence component in the reference voltage, φ cirV Indicates the initial phase angle of the double frequency negative sequence component in the reference voltage.

[0153] The arithmetic mean of the submodule capacitor current is calculated from the bridge arm modulation wave and the bridge arm current:

[0154]

[0155] Furthermore, after ignoring the DC component in the submodule capacitor current, the arithmetic mean of the submodule capacitor voltage can be calculated based on the capacitance of the submodule capacitor and the arithmetic mean of the submodule capacitor current:

[0156]

[0157] Taking into account the internal calculation delay of the simulation software, the submodule capacitor voltage calculated by the above formula needs to be delayed by one simulation step before being brought into the calculation. The voltage of the upper bridge arm of phase A of the MMC can be obtained as follows:

[0158]

[0159] Since the same electrical quantity of the upper and lower bridge arms of each phase of the MMC is symmetrical, the voltage u of the lower bridge arm in the same phase can be directly obtained from the voltage of the upper bridge arm. Ba Taking into account the internal calculation delay of the simulation software, the bridge arm voltage calculated above needs to be delayed by one simulation step to obtain the accurate bridge arm voltage.

[0160]

[0161] According to the expanded result of formula 32, after considering the harmonic disturbance injected from the AC side and the DC side, the common mode voltage of the MMC will couple a frequency of -f p -f1 and f p -3f1 harmonic components. However, the DC side of the MMC only contains DC components and the frequency f p The harmonic disturbance component of -f1, combined with the common-mode circuit, shows that the harmonic component in the common-mode voltage will generate a harmonic component of the same frequency in the internal circulating current of the MMC. The internal circulating current of the MMC can be expressed as:

[0162] i cira (t) = I cir2 cos[-(ω p +ω1)t+φ cir2 ]+I cir3 cos[(ω p -3ω1)t+φ cir3 ] (33)

[0163] Further, according to the circulating current suppression control structure, the above-mentioned harmonic circulating current will generate frequency-f p -f1and f p -3f1reference voltage components. Therefore, the bridge arm modulation wave can be rewritten as:

[0164]

[0165] where V cir2 , V cir3 represent the amplitudes of the two harmonic components of frequency-f p -f1and f p -3f1in the reference voltage generated by the circulating current suppression control, and φ cirV2 , φ cirV3 represent the initial phase angles of the above-mentioned two harmonic components, respectively.

[0166] 2) Second iteration

[0167] According to the foregoing derivation, the MMC internal circulating current will additionally include harmonic components of frequency-f p -f1and f p -3f1, and the reference voltage will additionally include harmonic components of frequency-f p -f1and f p -3f1. Therefore, the bridge arm dynamics need to be iterated twice after the internal circulating current and the reference voltage are corrected. The arithmetic mean of the submodule capacitor currents calculated from the corrected bridge arm modulation wave and the bridge arm current can be represented as:

[0168]

[0169] After ignoring the DC component in the submodule capacitor current, the submodule capacitor voltage can be further obtained as:

[0170]

[0171] Considering the internal calculation delay of the simulation software, the submodule capacitor voltage calculated by the above formula is delayed by one simulation step before being brought into the calculation, and the upper bridge arm voltage of the A phase of the MMC can be obtained as:

[0172]

[0173] Since the same kind of electrical quantity of the upper and lower bridge arms of each phase is symmetrical, the lower bridge arm voltage u Ba (t) of the same phase can be directly obtained from the upper bridge arm voltage. Considering the internal calculation delay of the simulation software, the bridge arm voltage calculated above also needs to be delayed by one simulation step before the accurate bridge arm voltage can be obtained.

[0174] At this point, after two iterations, relatively accurate upper and lower bridge arm voltages can be obtained;

[0175] The differential-mode voltage and common-mode voltage of the MMC can be further calculated from the bridge arm voltage. The differential-mode voltage is actually the output voltage on the AC side of the MMC. The relationship between the differential-mode loop and the electrical quantities on both sides of the converter transformer can be used to establish an expression between the differential-mode voltage and the harmonics injected on the AC side. The common-mode voltage can be combined with the common-mode loop to establish an expression between the common-mode voltage and the harmonics injected on the DC side.

[0176] Step 9: Derivation of the overall impedance model

[0177] According to the single-phase topology diagram of MMC, the common mode circuit of MMC can be established as follows:

[0178]

[0179] According to the common-mode loop formula, the same-frequency components on both sides of the equation remain equal. Using the common-mode voltage derived in Step 8, we can determine the newly emerging harmonic components in the MMC's internal circulating current. Each harmonic circulating current component can be expressed using known electrical quantities and parameters.

[0180] Since the DC voltage only contains DC components and the frequency is f p -f1 harmonic disturbance component and the purpose of derivation is to obtain a three-port frequency coupled impedance model, so only the frequency f in the common mode voltage is concerned. p -f1 part. According to the bridge arm voltage derived in step 8, the common mode voltage frequency is f p -f1 component. Further combined with the common mode voltage loop, we can get:

[0181]

[0182] According to the single-phase topology diagram of MMC, the differential mode circuit of MMC can be established as follows:

[0183]

[0184] in, Indicates the differential mode voltage of the MMC. The differential mode voltage is also the potential of the virtual point between the upper and lower bridge arms of the MMC. It is called the output voltage of the MMC AC side.

[0185] Since the AC side of the MMC only contains the fundamental component and two frequency-coupled harmonic disturbance components, in order to facilitate the subsequent derivation of the three-port frequency-coupled impedance model, we will focus on the frequency f in the differential mode voltage. p and f p2 Further, by substituting the above derivation results of harmonic circulating current, we can get the frequency f pThe differential mode voltage component of is expressed as:

[0186]

[0187] in, Indicates frequency f p The MMC AC side output voltage phasor.

[0188] According to the derivation results, the frequency is 2f1-f p The relationship between the differential mode voltage component and the injected harmonic disturbance. In order to unify the representation of harmonic voltage and harmonic current, the frequency is 2f1-f p The differential mode voltage of is conjugated and expressed as:

[0189]

[0190] in, Indicates the frequency is 2f1-f p The conjugate of the MMC AC side output voltage phasor.

[0191] Combining Equation 39, Equation 41, and Equation 42, we can obtain the three-dimensional transfer function matrix of the MMC AC side output voltage and DC harmonic voltage:

[0192]

[0193] in,

[0194] Substituting the voltage and current relationship between the grid and valve sides of the converter transformer derived in step 5 into the differential mode loop shown in formula 40, the relationship between the output voltage on the AC side of the MMC and the injected harmonic disturbance can be obtained. After further considering the dynamics of the DC port, the three-dimensional transfer function matrix of the MMC AC and DC external characteristics can be obtained as follows:

[0195]

[0196] Combining Equation 43 and Equation 44, we can obtain:

[0197]

[0198] in,

[0199] According to the above formula, we can get:

[0200]

[0201] In summary, after deducing the MMC control process, internal bridge arm dynamics, and external circuits, a broadband three-port frequency-coupled impedance model for the MMC was ultimately developed. By taking into account factors such as MMC control delay, signal transmission and calculation delays in the simulation software, and internal circulating currents and their suppression control within the MMC, the resulting model ensures accuracy across a wide frequency range. Furthermore, this model establishes the coupling relationship between the AC and DC sides of the converter, laying the foundation for stability analysis of flexible DC systems.

[0202] Next, a device for establishing an MMC broadband three-port frequency-coupled impedance model according to an embodiment of the present application will be described with reference to the accompanying drawings.

[0203] Figure 4 4 is a block diagram of a device for establishing an MMC broadband three-port frequency-coupled impedance model according to an embodiment of the present application.

[0204] like Figure 4 As shown, the MMC broadband three-port frequency-coupled impedance model establishment device 10 includes: a derivation module 100 , a solution module 200 and a modeling module 300 .

[0205] Among them, the derivation module 100 is used to establish a three-dimensional transfer function matrix of the internal control link of the MMC, and determine the reference voltage generated by the internal control link of the MMC based on the three-dimensional transfer function matrix; the solution module 200 is used to perform a secondary iterative solution of the dynamics of the internal bridge arm of the MMC based on the reference voltage and the disturbance components of the AC side and the DC side of the MMC to obtain the actual output voltage of the upper bridge arm and the lower bridge arm of the MMC; the modeling module 300 is used to calculate the differential mode voltage and common mode voltage of the MMC according to the actual output voltage of the upper bridge arm and the lower bridge arm of the MMC, establish a differential mode voltage loop and a common mode voltage loop based on the differential mode voltage and the common mode voltage respectively, and use the differential mode voltage loop and the common mode voltage loop to establish a wide-band three-port frequency coupled impedance model of the MMC, and use the differential mode voltage loop and the common mode voltage loop to establish a wide-band three-port frequency coupled impedance model of the MMC for outputting the stability of the wide-band oscillation of the flexible direct current system.

[0206] Furthermore, the broadband three-port frequency-coupled impedance model is:

[0207]

[0208] Where Z represents the three-port frequency-coupled impedance matrix, Z11, Z22, and Z33 are self-impedances, representing the impedance at the two coupled frequencies on the AC side and the impedance at the DC harmonic frequency, respectively; the remaining matrix elements are mutual impedances, representing the impedance between different frequencies on the AC side or between AC and DC; Vp and Vp2 represent the harmonic voltage components of the two frequency couplings on the AC side, respectively, and ΔVdc represents the harmonic voltage components on the DC side; Ip and Ip2 represent the harmonic current components of the two frequency couplings on the AC side, respectively, and ΔIdc represents the harmonic current components on the DC side; frequency coupling means that the sum of the frequencies of the two harmonic voltage or harmonic current components is twice the power frequency, that is, fp+fp2=2f1, where f1 is the frequency of the fundamental component, and * indicates taking the conjugate.

[0209] Furthermore, the derivation module is further used to obtain the phase-locked loop dynamics, outer loop control dynamics, positive sequence current inner loop control dynamics, and negative sequence current inner loop control dynamics in the control link; and establish a three-dimensional transfer function matrix based on the phase-locked loop dynamics, outer loop control dynamics, positive sequence current inner loop control dynamics, and negative sequence current inner loop control dynamics.

[0210] Furthermore, the solution module is further used to perform a first iterative solution based on the reference voltage and the disturbance components on the AC side and the DC side of the MMC to obtain the harmonic circulating current components; and perform a second iterative solution of the bridge arm dynamics based on the harmonic circulating current components to generate the actual output voltages of the upper and lower bridge arms of the MMC.

[0211] Furthermore, it also includes: an injection module, which is used to inject a preset signal harmonic disturbance on the AC side and DC side of the MMC at the same time before performing a secondary iterative solution of the MMC internal bridge arm dynamics based on the reference voltage and the disturbance components on the AC side and DC side of the MMC to generate the disturbance components on the AC side and DC side of the MMC.

[0212] It should be noted that the above explanation of the method for establishing the MMC broadband three-port frequency-coupled impedance model embodiment is also applicable to the apparatus for establishing the MMC broadband three-port frequency-coupled impedance model of this embodiment, and will not be repeated here.

[0213] According to the device for establishing the MMC broadband three-port frequency-coupled impedance model proposed in the embodiment of the present application, after derivation of the MMC control link, internal bridge arm dynamics and external circuit, the broadband three-port frequency-coupled impedance model of the MMC is finally formed. Since all factors such as the MMC control delay, the transmission and calculation delay of the signal in the simulation software, and the internal circulating current and circulating current suppression control of the MMC are taken into consideration, the obtained model can ensure accuracy within a broadband range. At the same time, the model constructs the coupling relationship between the AC side and the DC side of the converter, laying the foundation for the stability analysis of the flexible DC system.

[0214] Figure 5A structural schematic diagram of an electronic device is provided in the embodiments of the present application. The electronic device can include

[0215] The memory 501, the processor 502, and the computer program stored in the memory 501 and executable on the processor 502.

[0216] The processor 502 implements the method for establishing the MMC wideband three-port frequency coupling impedance model provided in the above embodiments when executing the program.

[0217] Further, the electronic device further includes

[0218] The communication interface 503 is used for communication between the memory 501 and the processor 502.

[0219] The memory 501 is used for storing the computer program executable on the processor 502.

[0220] The memory 501 can include a high-speed RAM (Random Access Memory) memory, and can also include a nonvolatile memory, for example, at least one disk memory.

[0221] If the memory 501, the processor 502, and the communication interface 503 are independently implemented, the communication interface 503, the memory 501, and the processor 502 can be connected to each other through a bus and complete communication between each other. The bus can be an ISA (Industry Standard Architecture) bus, a PCI (Peripheral Component) bus, or an EISA (Extended Industry Standard Architecture) bus, etc. The bus can be divided into an address bus, a data bus, a control bus, etc. For the convenience of representation, Figure 5 Only one thick line is used in the figure, but it does not mean that there is only one bus or only one type of bus.

[0222] Optionally, in a specific implementation, if the memory 501, the processor 502, and the communication interface 503 are integrated on a chip, the memory 501, the processor 502, and the communication interface 503 can complete communication between each other through an internal interface.

[0223] The processor 502 can be a CPU (Central Processing Unit), or an ASIC (Application Specific Integrated Circuit), or one or more integrated circuits configured to implement the embodiments of the present application.

[0224] An embodiment of the present application further provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-mentioned method for establishing the MMC broadband three-port frequency-coupled impedance model.

[0225] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" 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 can be combined in any one or N embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine different embodiments or examples described in this specification and features of different embodiments or examples without contradiction.

[0226] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be understood to indicate or imply relative importance or implicitly specify the number of technical features indicated. Thus, a feature specified as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of this application, "N" means at least two, for example, two, three, etc., unless otherwise specifically defined.

[0227] Any process or method description in a flowchart or otherwise described herein may be understood to represent a module, fragment or portion of code comprising one or more executable instructions for implementing the steps of a custom logical function or process, and the scope of the preferred embodiments of the present application includes alternative implementations in which functions may be performed out of the order shown or discussed, including performing functions in a substantially simultaneous manner or in reverse order depending on the functions involved, which should be understood by those skilled in the art to which the embodiments of the present application belong.

[0228] It should be understood that various parts of the present application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiment, the N steps or methods can be implemented using software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented using hardware, as in another embodiment, any one of the following technologies known in the art or a combination thereof can be used: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application-specific integrated circuit having a suitable combination of logic gate circuits, a programmable gate array, a field programmable gate array, etc.

[0229] Those skilled in the art will understand that all or part of the steps in the method of the above embodiment can be completed by instructing related hardware through a program, and the program can be stored in a computer-readable storage medium. When the program is executed, it includes one or a combination of the steps of the method embodiment.

[0230] Although the embodiments of the present application have been shown and described above, it can be understood that the above embodiments are exemplary and cannot be understood as limitations on the present application. Ordinary technicians in this field can change, modify, replace and modify the above embodiments within the scope of the present application.

Claims

1. A method for establishing an MMC broadband three-port frequency-coupled impedance model, characterized in that: The following steps are involved: Acquiring phase-locked loop dynamics, outer loop control dynamics, positive sequence current inner loop control dynamics, and negative sequence current inner loop control dynamics in the control link; establishing a three-dimensional transfer function matrix based on the phase-locked loop dynamics, outer loop control dynamics, positive sequence current inner loop control dynamics, and negative sequence current inner loop control dynamics, and determining a reference voltage generated by the MMC internal control link based on the three-dimensional transfer function matrix; Performing a first iterative solution based on the reference voltage and the disturbance components on the AC side and the DC side of the MMC to obtain harmonic circulating current components; Performing a second iterative solution of the bridge arm dynamics based on the harmonic circulating current component to generate actual output voltages of the upper bridge arm and the lower bridge arm of the MMC; Calculating the differential-mode voltage and common-mode voltage of the MMC based on the actual output voltages of the upper bridge arm and the lower bridge arm of the MMC, establishing a differential-mode voltage loop and a common-mode voltage loop based on the differential-mode voltage and the common-mode voltage, respectively, and using the differential-mode voltage loop and the common-mode voltage loop to establish a broadband three-port frequency-coupled impedance model of the MMC for outputting the stability of broadband oscillation of the flexible direct current system; The broadband three-port frequency coupled impedance model is: Where Z represents the three-port frequency-coupled impedance matrix, Z11, Z22, and Z33 are self-impedances, representing the impedance at the two coupled frequencies on the AC side and the impedance at the DC harmonic frequency, respectively; the remaining matrix elements are mutual impedances, representing the impedance between different frequencies on the AC side or between AC and DC; Vp and Vp2 represent the harmonic voltage components of the two coupled frequencies on the AC side, respectively, and ΔVdc represents the harmonic voltage components on the DC side; Ip and Ip2 represent the harmonic current components of the two coupled frequencies on the AC side, respectively, and ΔIdc represents the harmonic current components on the DC side; Frequency coupling means that the sum of the frequencies of the two harmonic voltage or harmonic current components is twice the power frequency, that is, fp+fp2=2f1, f1 is the frequency of the fundamental component, and * indicates conjugation.

2. The method according to claim 1, characterized in that Before performing a secondary iterative solution of the MMC internal bridge arm dynamics based on the reference voltage and the disturbance components of the AC side and the DC side of the MMC, the method further includes: A preset signal harmonic disturbance is injected simultaneously into the AC side and the DC side of the MMC to generate disturbance components on the AC side and the DC side of the MMC.

3. A device for establishing an MMC broadband three-port frequency-coupled impedance model, characterized in that: include: a derivation module for obtaining phase-locked loop dynamics, outer loop control dynamics, positive sequence current inner loop control dynamics, and negative sequence current inner loop control dynamics in the control link; establishing a three-dimensional transfer function matrix based on the phase-locked loop dynamics, outer loop control dynamics, positive sequence current inner loop control dynamics, and negative sequence current inner loop control dynamics; and determining a reference voltage generated by the MMC internal control link based on the three-dimensional transfer function matrix; A solution module, configured to perform a first iterative solution based on the reference voltage and the disturbance components on the AC side and the DC side of the MMC to obtain a harmonic circulating current component; Performing a second iterative solution of the bridge arm dynamics based on the harmonic circulating current component to generate actual output voltages of the upper bridge arm and the lower bridge arm of the MMC; a modeling module, configured to calculate the differential-mode voltage and common-mode voltage of the MMC based on the actual output voltages of the upper bridge arm and the lower bridge arm of the MMC, establish a differential-mode voltage loop and a common-mode voltage loop based on the differential-mode voltage and the common-mode voltage, respectively, and establish a broadband three-port frequency-coupled impedance model of the MMC using the differential-mode voltage loop and the common-mode voltage loop, and establish a broadband three-port frequency-coupled impedance model of the MMC for outputting the stability of broadband oscillation of a flexible direct current system using the differential-mode voltage loop and the common-mode voltage loop; The broadband three-port frequency coupled impedance model is: Where Z represents the three-port frequency-coupled impedance matrix, Z11, Z22, and Z33 are self-impedances, representing the impedance at the two coupled frequencies on the AC side and the impedance at the DC harmonic frequency, respectively; the remaining matrix elements are mutual impedances, representing the impedance between different frequencies on the AC side or between AC and DC; Vp and Vp2 represent the harmonic voltage components of the two coupled frequencies on the AC side, respectively, and ΔVdc represents the harmonic voltage components on the DC side; Ip and Ip2 represent the harmonic current components of the two coupled frequencies on the AC side, respectively, and ΔIdc represents the harmonic current components on the DC side; Frequency coupling means that the sum of the frequencies of the two harmonic voltage or harmonic current components is twice the power frequency, that is, fp+fp2=2f1, f1 is the frequency of the fundamental component, and * indicates conjugation.

4. The device according to claim 3, characterized in that Also includes: The injection module is used to inject a preset signal harmonic disturbance simultaneously on the AC side and the DC side of the MMC before performing a secondary iterative solution of the MMC internal bridge arm dynamics based on the reference voltage and the disturbance components on the AC side and the DC side of the MMC to generate the disturbance components on the AC side and the DC side of the MMC.

5. An electronic device, characterized in that: include: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the method for establishing the MMC broadband three-port frequency-coupled impedance model according to any one of claims 1 to 2.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that: The program is executed by a processor to implement the method for establishing the MMC broadband three-port frequency-coupled impedance model according to any one of claims 1 to 2.

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