A method for modeling and stability analysis of sequence admittance of modular multilevel converter

Abstract

The application discloses a sequence admittance modeling and stability analysis method of a modular multilevel converter, belongs to the field of power system control, carries out two-port equivalence on the modular multilevel converter, obtains a single-phase two-port network with one end being an alternating current port and the other end being a direct current port; adds disturbance in the single-phase two-port network, obtains a linearized model, eliminates intermediate variables of the linearized model, and obtains a single-input multi-output admittance module under a two-port view; the admittance module is used to represent coupling effects of the alternating current port and the direct current port, to obtain self-admittance after considering alternating current-direct current coupling; frequency coupling caused by grid impedance is considered in a controlled source equivalent mode to obtain additional admittance after considering frequency coupling; and the self-admittance after considering alternating current-direct current coupling and the additional admittance after considering frequency coupling are added to obtain a sequence admittance model of the modular multilevel converter. The application can accurately model the modular multilevel converter under grid-connected conditions.

Description

Technical Field

[0001] This invention belongs to the field of power system control, and more specifically, relates to a method for sequential impedance modeling and stability analysis of modular multilevel converters. Background Technology

[0002] Since its inception, the modular multilevel converter (MMC) has become the mainstream converter topology in fields such as flexible DC transmission, renewable energy grid integration, offshore wind power integration, and power electronic grids due to its excellent scalability, redundancy, and high power density. At the grid connection point, if the MMC impedance interacts unfavorably with the grid impedance, broadband oscillations can easily occur. Numerous engineering accidents have shown that the uncertainty of the grid impedance, along with insufficient open-loop gain of the controller and harmonic coupling, can cause control instability, output oscillations, submodule voltage fluctuations, and even system instability in the MMC. The impedance method, due to its clear and explicit physical meaning, is currently the academically recognized method for analyzing broadband oscillation problems and has been applied in practical engineering.

[0003] Existing impedance modeling methods mainly include dq Impedance method and sequence impedance method. dq Impedance models, established based on a synchronous rotating coordinate system, can transform three-phase steady-state quantities into DC quantities, thereby revealing the impact of controllers such as current loops, phase-locked loops, and virtual impedances on system dynamics. This model can be used to analyze low-frequency oscillations, control coupling, and the effects of internal control parameters on stability. However... dq Impedance is essentially a coupled two-dimensional multiple-input multiple-output system, and in large-scale systems, a unified coordinate system is required, making it inconvenient to use directly in engineering applications. Sequence impedance models, based on the symmetrical component method, decompose the three-phase system into positive-sequence and negative-sequence components, thus clearly characterizing the dynamic characteristics of the system at different sequence paths. For scenarios where the power grid is approximately balanced, positive-sequence impedance can describe the main grid-connected behavior, simplifying the originally complex three-phase converter dynamics into a single-input single-output model, facilitating the application of classic stability criteria such as the Nyquist model. Furthermore, sequence impedance is consistent with traditional power grid equivalent impedance, line impedance, and transformer models, making it particularly suitable for engineering testing, field measurement, and standardized evaluation. However, with the increasing complexity of converter control strategies, such as the introduction of phase-locked loops, cross-coupled current loops, and nonlinear control methods, significant positive and negative sequence frequency coupling occurs, making a single positive-sequence impedance insufficient to fully characterize the system's dynamic characteristics. Moreover, traditional sequence impedance methods neglect the influence of DC port bus dynamics and AC port grid impedance, and insufficient model accuracy may lead to misjudgments in stability analysis.

[0004] In summary, existing impedance modeling methods suffer from the technical problem of failing to accurately model modular multilevel converters under grid-connected conditions. Summary of the Invention

[0005] To address the aforementioned deficiencies or improvement needs of existing technologies, this invention provides a method for sequence impedance modeling and stability analysis of modular multilevel converters, thereby solving the technical problem that existing impedance modeling methods are difficult to accurately model modular multilevel converters under grid-connected conditions.

[0006] To achieve the above objectives, according to a first aspect of the present invention, a method for modeling the sequence impedance of a modular multilevel converter is provided, comprising the following steps:

[0007] (1) Perform two-port equivalence on the modular multilevel converter to obtain a single-phase two-port network with one end being an AC port and the other end being a DC port;

[0008] (2) Add a disturbance to the single-phase two-port network to obtain a linearized model. Eliminate the intermediate variables of the linearized model to obtain a single-input multiple-output admittance module from the perspective of two-port network.

[0009] (3) The coupling effect of AC port and DC port is characterized by the admittance module to obtain the self admittance after considering AC-DC coupling. The frequency coupling generated by the grid impedance is considered by the controlled source equivalent method to obtain the additional admittance after considering frequency coupling. The self admittance after considering AC-DC coupling and the additional admittance after considering frequency coupling are added to obtain the sequence impedance model of the modular multilevel converter.

[0010] Furthermore, the self-admittance considering AC / DC coupling is the positive-sequence self-admittance considering AC / DC coupling, and the additional admittance considering frequency coupling is the additional positive-sequence admittance considering frequency coupling. The positive-sequence self-admittance considering AC / DC coupling and the additional positive-sequence admittance considering frequency coupling are added together to obtain the positive-sequence admittance. The negative conjugate of the positive-sequence admittance is taken to obtain the negative-sequence admittance. The positive-sequence admittance and the negative-sequence admittance constitute the sequence-inductance reactance model of the modular multilevel converter.

[0011] Furthermore, the self-admittance considering AC / DC coupling includes positive-sequence self-admittance and negative-sequence self-admittance considering AC / DC coupling, and the additional admittance considering frequency coupling includes additional positive-sequence admittance and additional negative-sequence admittance considering frequency coupling. The positive-sequence self-admittance considering AC / DC coupling and the additional positive-sequence admittance considering frequency coupling are added together to obtain the positive-sequence admittance, and the negative-sequence self-admittance considering AC / DC coupling and the additional negative-sequence admittance considering frequency coupling are added together to obtain the negative-sequence admittance. The positive-sequence admittance and the negative-sequence admittance constitute the sequence-inductance reactance model of the modular multilevel converter.

[0012] Furthermore, the positive-sequence self-admittance considering AC / DC coupling is:

[0013]

[0014] in, s For the perturbation frequency, The perturbation frequency deviates from the fundamental frequency by a factor of two. Indicates the perturbation frequency as s When considering the positive-sequence self-admittance after AC / DC coupling, When the disturbance frequency is s, the positive-sequence self-admittance after AC / DC coupling is ignored. Let be the transfer admittance of the DC port response to the AC port positive-sequence disturbance after neglecting AC-DC coupling when the disturbance frequency is s. When the disturbance frequency deviates from the fundamental frequency by a factor of one, the transfer admittance of the positive-sequence response of the AC port to the DC port disturbance after AC-DC coupling is neglected. The DC bus capacitance impedance is given when the disturbance frequency deviates from the fundamental frequency by a factor of two. When the disturbance frequency deviates from the fundamental frequency by a factor of one, the DC port self-admittance after AC-DC coupling is ignored.

[0015] Furthermore, the additional positive-sequence admittance considering frequency coupling is:

[0016]

[0017] in, s For the perturbation frequency, The perturbation frequency deviates from the fundamental frequency by twice. The perturbation frequency is s When considering the additional positive-sequence admittance after frequency coupling, The positive-sequence transfer admittance considering AC / DC coupling is given when the disturbance frequency deviates from twice the fundamental frequency. The perturbation frequency is s When considering the positive-sequence transfer admittance after AC / DC coupling, The positive-sequence self-admittance considering AC / DC coupling is given when the disturbance frequency deviates from twice the fundamental frequency. It is the admittance of the power grid connected to the AC port when the disturbance frequency deviates from twice the fundamental frequency.

[0018] Further, step (2) includes:

[0019] A first voltage perturbation is added to the AC port of a single-phase two-port network to obtain a linearized model of the AC port. A second voltage perturbation is added to the DC port of the single-phase two-port network to obtain a linearized model of the DC port. The linearized models of the AC port and the DC port together form the linearized model of the main circuit in the single-phase two-port network.

[0020] Multi-harmonic linearization is performed on the small-signal current of the bridge arm and the small disturbance of the first voltage to obtain the first linearization model. Multi-harmonic linearization is performed on the small-signal current of the bridge arm and the small disturbance of the second voltage to obtain the second linearization model. The first linearization model and the second linearization model constitute the linearization model of the control loop in the single-phase two-port network.

[0021] By eliminating intermediate variables in the linearized model of the main circuit and control loop in a single-phase two-port network, a single-input multiple-output admittance module from a two-port perspective is obtained.

[0022] Furthermore, the control loop in the single-phase two-port network includes phase-locked loop control, circulating current suppression control, constant current control, and constant DC voltage control.

[0023] Linearizing the phase-locked loop (PLL) control, the resulting linearized PLL control model is as follows:

[0024] ,

[0025] Where the linearization model is either the first linearization model or the second linearization model, This refers to either the first voltage small perturbation frequency or the second voltage small perturbation frequency. This refers to either a small voltage disturbance or a small voltage disturbance. For the small perturbation of the phase-locked angle after linearization, The imaginary unit, For the fundamental frequency, The perturbation frequency is s The closed-loop transfer function of time-locked loop control. , This refers to the grid-connected voltage amplitude. Characterizes the effect of the initial phase angle of the voltage during grid connection. The lag angle of the grid connection point voltage. It is a natural constant. The perturbation frequency is s Open-loop transfer function of time-locked loop control;

[0026] The closed-loop transfer function of phase-locked loop control is used in constant current control. The small-signal current of the bridge arm and the small disturbance of the first voltage are linearized by multiple harmonics to obtain the first linearized model. The small-signal current of the bridge arm and the small disturbance of the second voltage are linearized by multiple harmonics to obtain the second linearized model. The first linearized model and the second linearized model constitute the linearized model of constant current control.

[0027] The closed-loop transfer function of phase-locked loop control is used in circulating current control. Multi-harmonic linearization is performed on the small-signal current of the bridge arm and the small disturbance of the first voltage to obtain the first linearization model. Multi-harmonic linearization is performed on the small-signal current of the bridge arm and the small disturbance of the second voltage to obtain the second linearization model. The first linearization model and the second linearization model constitute the linearization model of circulating current control.

[0028] By combining the linearized model of constant current control with the linearized model of circulating current control, a linearized model of AC port control loop is obtained.

[0029] By linearizing the constant DC voltage control, a linearized model of constant DC voltage control is obtained.

[0030] According to a second aspect of the present invention, a sequential impedance modeling system for a modular multilevel converter is provided, comprising a processor for executing processing steps of a sequential impedance modeling method for a modular multilevel converter.

[0031] According to a third aspect of the invention, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the processing steps of a sequential impedance modeling method for a modular multilevel converter as described in any one of claims 1 to 7.

[0032] According to a fourth aspect of the present invention, a stability analysis method for a modular multilevel converter is provided, comprising: constructing a sequential reactance model using a sequential reactance modeling method for a modular multilevel converter to obtain the original power grid network not connected to the converter; performing stability analysis on the original power grid network and the modular multilevel converter respectively; if both are stable, connecting the modular multilevel converter to the original power grid network; if they are unstable, considering it as power system instability caused by the modular multilevel converter.

[0033] In summary, compared with the prior art, the above-described technical solutions conceived by this invention can achieve the following beneficial effects:

[0034] (1) This invention performs two-port equivalence on modular multilevel converters, reducing the number of control variables and lowering the system's dimensionality and complexity. Applying disturbances to a single-phase two-port network is an effective analysis method in sequence-induced impedance modeling, which can significantly improve the model's accuracy and practicality. Disturbance injection provides rich data support for modeling by actively stimulating the system's dynamic characteristics. Eliminating intermediate variables in the linearized model yields a single-input multi-output admittance module from a two-port perspective, which can fully reveal the coupling characteristics between multiple variables within the modular multilevel converter. Using the admittance module to characterize the coupling effect between the AC and DC ports, the self-admittance after considering AC-DC coupling can be accurately obtained, providing a precise mathematical basis for the system's oscillation analysis and stability assessment. Considering the frequency coupling generated by grid impedance through controlled source equivalence simplifies complex coupling analysis. Integrating the admittance module through sequence-induced impedance modeling allows for a more intuitive characterization of the positive-sequence and negative-sequence dynamic characteristics. It can not only accurately account for the influence of different control strategies on the system's frequency domain characteristics but also reflect AC-DC coupling and frequency coupling, enabling accurate modeling of the modular multilevel converter under grid-connected conditions.

[0035] (2) When performing sequential impedance modeling in this invention, the negative sequence admittance can be obtained by taking the negative conjugate of the positive sequence admittance, or the negative sequence self-admittance after considering AC / DC coupling can be added to the additional negative sequence admittance after considering frequency coupling to obtain the negative sequence admittance. This shows that the sequential impedance modeling method of this invention is diverse. This invention uses the form of negative feedback of transfer function to consider the influence of AC / DC coupling on positive sequence self-admittance. The physical meaning is clear, and the formula accurately accounts for the additional coupling term of positive sequence self-admittance under AC / DC coupling. Frequency coupling is considered in the form of equivalent circuit correction. The positive and negative sequence coupling frequencies are included in the self-admittance using the formula, which realizes the dimensionality reduction of the model and thus enables accurate stability analysis.

[0036] (3) In the process of modeling and linearizing the phase-locked loop, this invention considers the influence of the initial phase angle of the voltage during grid connection, through... To characterize the impact of the initial phase angle of the voltage during grid connection, accurate modeling of different initial phase angles for grid connection can be achieved. Applying the phase-locked loop (PLL) linearization results to constant current control yields the differential-mode small-signal linearization results for the AC port. This invention accurately considers the impact of multiple harmonics when modeling constant current control and circulating current control, and can accurately reflect the influence of the control strategies unique to modular multilevel converters.

[0037] (4) The sequence-lead reactance model obtained by this invention has high accuracy, high interpretability, and good scalability, providing a systematic and generalizable theoretical tool for the stability analysis of modular multilevel converters in scenarios such as weak power grids. This invention provides a stability analysis method that uses the sequence-lead reactance modeling method to obtain an accurate and computationally inefficient sequence-lead reactance model, and performs stability analysis on unconnected original power grid networks and modular multilevel converters. The judgment process has low computational complexity and high accuracy. Attached Figure Description

[0038] Figure 1 This is a flowchart of a sequential impedance modeling method for a modular multilevel converter provided in an embodiment of the present invention.

[0039] Figure 2(a) is the main circuit diagram of the modular multilevel converter provided in the embodiment of the present invention.

[0040] Figure 2(b) is a schematic diagram of a sub-module of the modular multilevel converter provided in an embodiment of the present invention.

[0041] Figure 3(a) is a schematic diagram of the positive sequence self-impedance amplitude of a modular multilevel converter considering AC / DC coupling provided in an embodiment of the present invention.

[0042] Figure 3(b) is a schematic diagram of the positive sequence self-impedance phase of a modular multilevel converter considering AC / DC coupling provided in an embodiment of the present invention.

[0043] Figure 3(c) is a schematic diagram of the positive sequence mutual impedance amplitude of the modular multilevel converter under AC / DC coupling provided in the embodiment of the present invention.

[0044] Figure 3(d) is a schematic diagram of the positive sequence mutual impedance phase of a modular multilevel converter considering AC / DC coupling provided in an embodiment of the present invention.

[0045] Figure 4 This is a comparison diagram showing whether frequency coupling is taken into account in the modular multilevel converter under the short-circuit comparison condition provided in the embodiments of the present invention.

[0046] Figure 5 This is a diagram of the AC port current after grid connection provided in an embodiment of the present invention. Detailed Implementation

[0047] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0048] In this invention, the terms "first," "second," etc. (if present) in the invention and the accompanying drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence.

[0049] like Figure 1 As shown, a method for modeling the sequence impedance of a modular multilevel converter includes the following steps:

[0050] (1) Perform two-port equivalence on the modular multilevel converter to obtain a single-phase two-port network with one end being an AC port and the other end being a DC port;

[0051] (2) Add a disturbance to the single-phase two-port network to obtain a linearized model. Eliminate the intermediate variables of the linearized model to obtain a single-input multiple-output admittance module from the perspective of two-port network.

[0052] (3) The coupling effect of AC port and DC port is characterized by the admittance module to obtain the self admittance after considering AC-DC coupling. The frequency coupling generated by the grid impedance is considered by the controlled source equivalent method to obtain the additional admittance after considering frequency coupling. The self admittance after considering AC-DC coupling and the additional admittance after considering frequency coupling are added to obtain the sequence impedance model of the modular multilevel converter.

[0053] It should be understood that, although Figure 1 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated in this invention, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Furthermore, Figure 1 At least a portion of it may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but may be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but may be executed in turn or alternately with other steps or at least a portion of the sub-steps or stages of other steps.

[0054] Example 1

[0055] A method for modeling the sequence impedance of a modular multilevel converter includes the following steps:

[0056] (1) Perform two-port equivalence on the modular multilevel converter to obtain a single-phase two-port network with one end being an AC port and the other end being a DC port;

[0057] (2) Add a disturbance to the single-phase two-port network to obtain a linearized model. Eliminate the intermediate variables of the linearized model to obtain a single-input multiple-output admittance module from the perspective of two-port network.

[0058] (3) The coupling effect of AC port and DC port is characterized by the admittance module to obtain the self admittance after considering AC-DC coupling. The frequency coupling generated by the grid impedance is considered by the controlled source equivalent method to obtain the additional admittance after considering frequency coupling. The self admittance after considering AC-DC coupling and the additional admittance after considering frequency coupling are added to obtain the sequence impedance model of the modular multilevel converter.

[0059] The specific operation of the two-port equivalent is as follows: the three-phase network of the AC port is not independent of each other, and the disturbance of each phase can be expressed as positive sequence, negative sequence and zero sequence components using the symmetrical component method, as shown below:

[0060]

[0061] in, , , This represents a small disturbance in the three-phase voltage. , , To obtain the positive-sequence, negative-sequence, and zero-sequence component amplitudes using the symmetric component method, For small perturbation frequencies, , , The initial phase angles of the disturbances for the positive-sequence, negative-sequence, and zero-sequence components are given. For time. Therefore, only the positive sequence, negative sequence and zero sequence components of phase a need to be considered to obtain the complete three-phase information, thus obtaining a single-phase two-port network with one end as an AC port and the other end as a DC port.

[0062] Specifically, step (2) includes:

[0063] A small voltage disturbance is introduced into the AC port of a single-phase two-port network. The linearized model of the AC port is obtained:

[0064]

[0065] in, This is the small-signal voltage of the bridge arm capacitor. For small signal current in the bridge arm, For a small modulation ratio signal, This is the steady-state voltage of the bridge arm capacitor. For the steady-state current of the bridge arm, This is the steady-state value of the modulation ratio. The equivalent impedance of the bridge arm capacitance is... The equivalent impedance of the bridge arm inductance, This represents convolution.

[0066]

[0067]

[0068] in The equivalent capacitance of the bridge arm. For bridge arm inductance, This is the equivalent bridge arm inductance and resistance value. This refers to the frequency of small-signal voltage perturbation. For the fundamental frequency, The coefficient matrix modified for the bridge arm admittance matrix. , It is a diagonal matrix. k It is a positive integer not greater than g.

[0069] A second voltage perturbation is introduced into the DC port of a single-phase two-port network. The linearized model of the DC port is obtained:

[0070]

[0071] The linearized models of the AC and DC ports constitute the linearized model of the main circuit in a single-phase two-port network.

[0072] Multi-harmonic linearization is performed on the small-signal current of the bridge arm and the small disturbance of the first voltage to obtain the first linearization model. Multi-harmonic linearization is performed on the small-signal current of the bridge arm and the small disturbance of the second voltage to obtain the second linearization model (the second linearization model is established in the same way as the first linearization model, only the disturbance added is different). The first linearization model and the second linearization model constitute the linearization model of the control loop in the single-phase two-port network.

[0073] By eliminating intermediate variables in the linearized model of the main circuit and control loop in a single-phase two-port network, a single-input multiple-output admittance module from a two-port perspective is obtained.

[0074] As shown in Figure 2(a), in the figure I dc This refers to the DC port current. V dc This is the DC port voltage; v a , v b , v c These represent the AC voltages of phases a, b, and c, respectively. i a , i b , i c These represent the alternating currents of phases a, b, and c, respectively. i au , ibu , i cu These represent the upper bridge arm currents of phases a, b, and c, respectively. i av , i bv , i cv These represent the lower bridge arm currents of phases a, b, and c, respectively. v au , v bu , v cu These represent the total output voltages of the upper bridge arm submodules for phases a, b, and c, respectively. v av , v bv , v cv These represent the total output voltages of the lower bridge arm submodules for phases a, b, and c, respectively. The variable subscript "u" represents the upper bridge arm, and "v" represents the lower bridge arm. As shown in Figure 2(b), the half-bridge submodule consists of two IGBTs (T1 and T2) and a submodule capacitor C. SM The circuit consists of two diodes, D1 and D2, which are anti-parallel freewheeling diodes of T1 and T2, respectively.

[0075] The control loop includes phase-locked loop control, circulating current suppression control, constant current control, and constant DC voltage control.

[0076] Linearize the phase-locked loop:

[0077] ,

[0078]

[0079] Where the linearization model is either the first linearization model or the second linearization model, This refers to either the first voltage small perturbation frequency or the second voltage small perturbation frequency. This refers to either a small voltage disturbance or a small voltage disturbance. For the small perturbation of the phase-locked angle after linearization, The imaginary unit, For the fundamental frequency, The perturbation frequency is s The closed-loop transfer function of time-locked loop control. , This refers to the grid-connected voltage amplitude. Characterizes the effect of the initial phase angle of the voltage during grid connection. The lag angle of the grid connection point voltage. It is a natural constant. Let be the open-loop transfer function of the phase-locked loop control when the disturbance frequency is s. It is the transfer function from a small voltage perturbation to a small phase-locked angle perturbation.

[0080] Using the phase-locked loop linearization result for constant current control yields the differential-mode small-signal linearization result for the AC port. As shown below, in the formula, Both are (2g+1)×(2g+1) matrices, representing the first and second matrices, and all elements except those described below are 0.

[0081]

[0082]

[0083]

[0084] in, For modulo function, k A positive integer not greater than g. For AC current control, the transfer function is... For constant current control, the decoupling coefficient is... The fundamental component of the bridge arm current under steady state. The conjugate of the fundamental component of the bridge arm current under steady state. The fundamental component of the modulation ratio in steady state. The fundamental component of the modulation ratio is the conjugate of the modulation ratio in steady state. This is the steady-state value of the DC voltage.

[0085] Using the results obtained from the phase-locked loop (PLL) for circulating current control, the common-mode small-signal linearization result of the AC port can be obtained. As shown below, in the formula, All are (2g+1)×(2g+1) matrices, representing the third and fourth matrices. Except for the elements described below, all other elements are 0.

[0086]

[0087]

[0088]

[0089] in, The transfer function for circulating current suppression control is... The steady-state current is the second harmonic component of the bridge arm current. The steady-state condition is the conjugate of the second harmonic component of the bridge arm current. The modulation ratio of the second harmonic component in steady state. The modulation ratio is the conjugate of the second harmonic component in steady state. This is the decoupling coefficient for the circulating flow control.

[0090] Furthermore, the linearization results of the differential-mode and common-mode small-signal signals can be used to obtain the linearization results of the AC port control loop. as follows:

[0091]

[0092] in and These are the linearization results related to the small current signal and the small voltage signal, respectively.

[0093] Furthermore, the linearization of the constant DC voltage control can be obtained as follows:

[0094]

[0095] In the formula, The matrix is ​​(2g+1)×(2g+1), where all elements except those mentioned above are 0. This is the transfer function for constant DC voltage control.

[0096] Based on the linearization results of the main circuit loop and the control loop, a single-input multiple-output admittance module can be obtained. By simultaneously solving the linearization results of the main circuit and the control loop to eliminate the small-signal quantities of modulation ratio and capacitor voltage, the final admittance matrix of the AC port, which neglects coupling, is obtained. The final admittance matrix obtained from the DC port, neglecting coupling. :

[0097]

[0098]

[0099] in, The left coefficient matrix of the AC port admittance. The right coefficient matrix of the AC port admittance. It is the identity matrix. This is the left coefficient matrix for the DC port. This is the right coefficient matrix for the DC port.

[0100] extract and The admittance module can be obtained from the admittance element information as follows:

[0101]

[0102]

[0103] Where g is the order of the highest harmonic being considered. To ignore the positive-sequence self-admittance after AC / DC coupling, To ignore the negative-sequence self-admittance of the AC port after AC-DC coupling To neglect the transfer admittance of the positive-sequence disturbance at the AC port to the negative-sequence current response after AC-DC coupling. To neglect the transfer admittance of the positive-sequence current response to the negative-sequence disturbance at the AC port after AC-DC coupling. To ignore the transfer admittance of the DC port response to the positive-sequence disturbance at the AC port after AC-DC coupling. To neglect the transfer admittance of the negative sequence disturbance at the AC port after AC-DC coupling on the DC port current response. To ignore the DC port self-admittance after AC / DC coupling. To ignore the transfer admittance of the positive-sequence response of the AC port due to the DC port disturbance after AC-DC coupling To ignore the transfer admittance of the DC-end disturbance response to the negative sequence current after AC-DC coupling, the superscript * indicates conjugate.

[0104] Furthermore, the self-admittance considering AC / DC coupling is the positive-sequence self-admittance considering AC / DC coupling, and the additional admittance considering frequency coupling is the additional positive-sequence admittance considering frequency coupling. The positive-sequence self-admittance considering AC / DC coupling and the additional positive-sequence admittance considering frequency coupling are added together to obtain the positive-sequence admittance. The negative conjugate of the positive-sequence admittance is taken to obtain the negative-sequence admittance. The positive-sequence admittance and the negative-sequence admittance constitute the sequence-inductance reactance model of the modular multilevel converter.

[0105] Furthermore, the self-admittance considering AC / DC coupling includes positive-sequence self-admittance and negative-sequence self-admittance considering AC / DC coupling, and the additional admittance considering frequency coupling includes additional positive-sequence admittance and additional negative-sequence admittance considering frequency coupling. The positive-sequence self-admittance considering AC / DC coupling and the additional positive-sequence admittance considering frequency coupling are added together to obtain the positive-sequence admittance, and the negative-sequence self-admittance considering AC / DC coupling and the additional negative-sequence admittance considering frequency coupling are added together to obtain the negative-sequence admittance. The positive-sequence admittance and the negative-sequence admittance constitute the sequence-inductance reactance model of the modular multilevel converter.

[0106] Furthermore, the positive-sequence self-admittance considering AC / DC coupling is:

[0107]

[0108] in, s For the perturbation frequency, The perturbation frequency deviates from the fundamental frequency by a factor of two. Indicates the perturbation frequency as s When considering the positive-sequence self-admittance after AC / DC coupling, When the disturbance frequency is s, the positive-sequence self-admittance after AC / DC coupling is ignored. Let be the transfer admittance of the DC port response to the AC port positive-sequence disturbance after neglecting AC-DC coupling when the disturbance frequency is s. When the disturbance frequency deviates from the fundamental frequency by a factor of one, the transfer admittance of the positive-sequence response of the AC port to the DC port disturbance after AC-DC coupling is neglected. The DC bus capacitance impedance is given when the disturbance frequency deviates from the fundamental frequency by a factor of two. When the disturbance frequency deviates from the fundamental frequency by a factor of one, the DC port self-admittance after AC-DC coupling is ignored.

[0109] Furthermore, the additional positive-sequence admittance considering frequency coupling is:

[0110]

[0111] in, s For the perturbation frequency, The perturbation frequency deviates from the fundamental frequency by twice. The perturbation frequency is s When considering the additional positive-sequence admittance after frequency coupling, The positive-sequence transfer admittance considering AC / DC coupling is given when the disturbance frequency deviates from twice the fundamental frequency. The perturbation frequency is s When considering the positive-sequence transfer admittance after AC / DC coupling, The positive-sequence self-admittance considering AC / DC coupling is given when the disturbance frequency deviates from twice the fundamental frequency. It is the admittance of the power grid connected to the AC port when the disturbance frequency deviates from twice the fundamental frequency.

[0112] Simulation experiments were conducted using the model established in Example 1. As shown in Figure 3(a), the measured values ​​of the positive-sequence self-impedance amplitude of the modular multilevel converter considering AC / DC coupling are basically consistent with the theoretical calculation values. Figure 3(b) shows the positive-sequence self-impedance phase diagram of the modular multilevel converter considering AC / DC coupling, and the measured values ​​are basically consistent with the theoretical calculation values. Figure 3(c) shows the positive-sequence mutual impedance amplitude of the modular multilevel converter considering AC / DC coupling, and the measured values ​​are basically consistent with the theoretical calculation values. Figure 3(d) shows the positive-sequence mutual impedance phase diagram of the modular multilevel converter considering AC / DC coupling, and the measured values ​​are basically consistent with the theoretical calculation values. Figure 4 This is a comparison chart showing whether frequency coupling is taken into account in modular multilevel converters under short-circuit conditions. Z p To account for the impedance curve of frequency coupling, Z ap To ignore the impedance curve for frequency coupling, Z gThe graph shows the power grid impedance curve, with frequency coupling considered. Z p and Z g An intersection will occur in the negative damping region, while the result of neglecting frequency coupling is negligible. Z ap and Z g The absence of intersection indicates that ignoring frequency coupling can lead to misjudgments in stability analysis. Figure 5 The diagram shows the AC port current after grid connection under short-circuit conditions with relatively small loads. The diagram shows that the AC port current oscillates and becomes unstable, which verifies the accuracy of stability analysis considering frequency coupling and the necessity of considering frequency coupling.

[0113] Embodiment 1 of this invention provides a sequence-lead impedance modeling method for a modular multilevel converter. By treating the modular multilevel converter as a two-port network with AC and DC ports, a clear and unified modeling framework can be constructed. Within this framework, small-signal perturbations are applied to the AC and DC ports respectively, allowing for the systematic derivation of linearized models of the main circuit and control system. Based on this linearized description, a single-input, multi-output admittance model is further obtained from a two-port perspective, enabling the clear revelation of the mutual influence between the AC and DC terminals and the coupling relationships between various frequency components.

[0114] Based on this, by characterizing the coupling characteristics of AC / DC ports using transfer functions and reflecting the coupling mechanism between different frequencies using equivalent circuits, an MMC sequence admittance / sequence impedance model that simultaneously covers port coupling and frequency coupling can be constructed. After introducing equivalent circuit corrections, this model can accurately characterize the dynamic characteristics and various coupling effects under different control strategies, providing a systematic and generalizable analytical tool for high-precision, interpretable frequency domain modeling of modular multilevel converters.

[0115] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for modeling the sequence impedance of a modular multilevel converter, characterized in that, Includes the following steps: (1) Perform two-port equivalence on the modular multilevel converter to obtain a single-phase two-port network with one end being an AC port and the other end being a DC port; (2) Add a disturbance to the single-phase two-port network to obtain a linearized model. Eliminate the intermediate variables of the linearized model to obtain a single-input multiple-output admittance module from the perspective of two-port network. (3) The coupling effect of AC port and DC port is characterized by the admittance module to obtain the self admittance after considering AC-DC coupling. The frequency coupling caused by grid impedance is considered by the controlled source equivalent method to obtain the additional admittance after considering frequency coupling. The self admittance after considering AC-DC coupling and the additional admittance after considering frequency coupling are added to obtain the sequence conductance model of the modular multilevel converter. The additional admittance considering frequency coupling is the additional positive-sequence admittance considering frequency coupling, or the additional admittance considering frequency coupling includes the additional positive-sequence admittance considering frequency coupling and the additional negative-sequence admittance considering frequency coupling. The additional positive-sequence admittance considering frequency coupling is: in, s For the perturbation frequency, The perturbation frequency deviates from the fundamental frequency by twice. The perturbation frequency is s When considering the additional positive-sequence admittance after frequency coupling, The positive-sequence transfer admittance considering AC / DC coupling is given when the disturbance frequency deviates from twice the fundamental frequency. The perturbation frequency is s When considering the positive-sequence transfer admittance after AC / DC coupling, The positive-sequence self-admittance considering AC / DC coupling is given when the disturbance frequency deviates from twice the fundamental frequency. The admittance of the power grid connected to the AC port when the disturbance frequency deviates from twice the fundamental frequency; The control loop in the single-phase two-port network includes phase-locked loop control, circulating current suppression control, constant current control, and constant DC voltage control. Linearizing the phase-locked loop (PLL) control, the resulting linearized PLL control model is as follows: ， Where the linearization model is either the first linearization model or the second linearization model, This refers to either the first voltage small perturbation frequency or the second voltage small perturbation frequency. This refers to either a small voltage disturbance or a small voltage disturbance. For the small perturbation of the phase-locked angle after linearization, The imaginary unit, For the fundamental frequency, The perturbation frequency is s The closed-loop transfer function of time-locked loop control. , This refers to the grid-connected voltage amplitude. Characterizes the effect of the initial phase angle of the voltage during grid connection. The lag angle of the grid connection point voltage. It is a natural constant. The perturbation frequency is s The open-loop transfer function of time-locked loop control.

2. The sequence impedance modeling method for a modular multilevel converter as described in claim 1, characterized in that, The self-admittance considering AC / DC coupling is the positive-sequence self-admittance considering AC / DC coupling, and the additional admittance considering frequency coupling is the additional positive-sequence admittance considering frequency coupling. The positive-sequence self-admittance considering AC / DC coupling and the additional positive-sequence admittance considering frequency coupling are added together to obtain the positive-sequence admittance. The negative conjugate of the positive-sequence admittance is taken to obtain the negative-sequence admittance. The positive-sequence admittance and the negative-sequence admittance constitute the sequence-inductance reactance model of the modular multilevel converter.

3. The sequence-lead impedance modeling method for a modular multilevel converter as described in claim 1, characterized in that, The self-admittance considering AC / DC coupling includes positive-sequence self-admittance and negative-sequence self-admittance considering AC / DC coupling. The additional admittance considering frequency coupling includes additional positive-sequence admittance and additional negative-sequence admittance considering frequency coupling. The positive-sequence self-admittance considering AC / DC coupling and the additional positive-sequence admittance considering frequency coupling are added together to obtain the positive-sequence admittance. The negative-sequence self-admittance considering AC / DC coupling and the additional negative-sequence admittance considering frequency coupling are added together to obtain the negative-sequence admittance. The positive-sequence admittance and the negative-sequence admittance constitute the sequence-inductance reactance model of the modular multilevel converter.

4. A sequence impedance modeling method for a modular multilevel converter as described in claim 2 or 3, characterized in that, The positive-sequence self-admittance considering AC / DC coupling is: in, s For the perturbation frequency, The perturbation frequency deviates from the fundamental frequency by a factor of two. Indicates the perturbation frequency as s When considering the positive-sequence self-admittance after AC / DC coupling, The perturbation frequency is s When neglecting the positive-sequence self-admittance after AC / DC coupling, The perturbation frequency is s When neglecting the transfer admittance of the positive-sequence disturbance at the AC port after AC-DC coupling on the DC port response, When the disturbance frequency deviates from the fundamental frequency by a factor of one, the transfer admittance of the positive-sequence response of the AC port to the DC port disturbance after AC-DC coupling is neglected. The DC bus capacitance impedance is given when the disturbance frequency deviates from the fundamental frequency by a factor of two. When the disturbance frequency deviates from the fundamental frequency by a factor of one, the DC port self-admittance after AC-DC coupling is ignored.

5. A method for modeling the sequence impedance of a modular multilevel converter as described in any one of claims 1-3, characterized in that, Step (2) includes: A first voltage perturbation is added to the AC port of a single-phase two-port network to obtain a linearized model of the AC port. A second voltage perturbation is added to the DC port of the single-phase two-port network to obtain a linearized model of the DC port. The linearized models of the AC port and the DC port together form the linearized model of the main circuit in the single-phase two-port network. Multi-harmonic linearization is performed on the small-signal current of the bridge arm and the small disturbance of the first voltage to obtain the first linearization model. Multi-harmonic linearization is performed on the small-signal current of the bridge arm and the small disturbance of the second voltage to obtain the second linearization model. The first linearization model and the second linearization model constitute the linearization model of the control loop in the single-phase two-port network. By eliminating intermediate variables in the linearized model of the main circuit and control loop in a single-phase two-port network, a single-input multiple-output admittance module from a two-port perspective is obtained.

6. The sequence-lead impedance modeling method for a modular multilevel converter as described in claim 5, characterized in that, The method further includes: The closed-loop transfer function of phase-locked loop control is used in constant current control. The small-signal current of the bridge arm and the small disturbance of the first voltage are linearized by multiple harmonics to obtain the first linearized model. The small-signal current of the bridge arm and the small disturbance of the second voltage are linearized by multiple harmonics to obtain the second linearized model. The first linearized model and the second linearized model constitute the linearized model of constant current control. The closed-loop transfer function of phase-locked loop control is used in circulating current control. Multi-harmonic linearization is performed on the small-signal current of the bridge arm and the small disturbance of the first voltage to obtain the first linearization model. Multi-harmonic linearization is performed on the small-signal current of the bridge arm and the small disturbance of the second voltage to obtain the second linearization model. The first linearization model and the second linearization model constitute the linearization model of circulating current control. By combining the linearized model of constant current control with the linearized model of circulating current control, a linearized model of AC port control loop is obtained. By linearizing the constant DC voltage control, a linearized model of constant DC voltage control is obtained.

7. A sequence-lead impedance modeling system for a modular multilevel converter, characterized in that, Includes a processor for performing processing steps of a sequential impedance modeling method for a modular multilevel converter as described in any one of claims 1 to 6.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the processing steps of the sequential impedance modeling method for a modular multilevel converter as described in any one of claims 1 to 6.

9. A stability analysis method for a modular multilevel converter, characterized in that, include: A sequential reactance model is constructed using the sequential reactance modeling method for a modular multilevel converter according to any one of claims 1-6, and the original power grid network without the converter is obtained. Stability analysis is performed on the original power grid network and the modular multilevel converter respectively. If both are stable, the modular multilevel converter is connected to the original power grid network. If they are unstable, it is considered that the power system instability is caused by the modular multilevel converter.

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