Time domain analysis method for island operation of modular multilevel converter based on grid

Abstract

The application discloses a time domain analysis method for island operation of a modular multilevel converter (MMGC) of a network construction type, and comprises the following steps: constructing AC and DC equivalent circuits of the MMGC in island operation; constructing a time domain steady-state analysis model of the MMGC considering coupling relations; and researching the influence of LC filters on capacitor voltages of sub-modules.The time domain analysis method has high precision under various working conditions, can replace time-consuming EMT simulation, can directly obtain amplitudes and phase angles of harmonic components of electrical quantities, and is very convenient for performance evaluation and harmonic analysis; based on the time domain analysis method, it is concluded that sub-module capacitors are highly related to filter capacitors, almost irrelevant to filter inductors, and the selection of the filter capacitors should consider load characteristics, and the method can be used for circuit parameter design.

Description

Technical Field

[0001] This invention belongs to the technical field of power converter model establishment and parameter design, specifically involving a method for islanded operation domain analysis of grid-type modular multilevel converters. Background Technology

[0002] Modular multilevel converters (MMGCs) are gaining increasing attention in both academia and industry. Compared to traditional grid-following converters, grid-forming converters can adjust their voltage and frequency according to the controlled object. With the development of grid control technology, their application scope has expanded from low-voltage scenarios to medium- and high-voltage scenarios. The modular multilevel converter (MMC) offers advantages such as excellent harmonic performance, lower switching losses, and the elimination of the need for direct series connection of semiconductor devices, making MMGC a feasible solution for medium- and high-voltage scenarios.

[0003] However, existing research on MMGCs is scarce. Although the steady-state characteristics of MMGCs can be obtained through electromagnetic transient (EMT) simulations or by referring to traditional MMCs, these methods have the following drawbacks: Modular multi-stage topologies typically contain a large number of switching devices and have complex control systems, making EMT simulations very time-consuming and unable to cover all operating conditions; for MMGCs, a set of LC filters is usually installed on the AC side to improve output voltage performance, but these LC filters may introduce coupling problems into the converter's internal electrical quantities, whereas traditional MMCs do not have these LC filters, so their impact on the MMGC operating point cannot be known from existing research; the controlled objects and connected loads of MMGCs differ from those of traditional MMCs, therefore, existing research cannot meet the requirements for performance evaluation, circuit parameter design, and semiconductor device selection for MMGCs.

[0004] In summary, MMGC has a wide range of applications, but existing research suffers from problems such as the time-consuming EMT simulation, the introduction of coupling in the internal electrical quantities of the AC side by the LC filter, and the inability to know its impact on the converter's operating point. Therefore, there is an urgent need to establish a time-domain steady-state analysis method for MMGC. Summary of the Invention

[0005] To overcome the problems existing in the prior art, the present invention aims to provide a method for islanded operation domain analysis of a grid-type modular multilevel converter, which can fully reflect the coupling relationship between the load, MMGC and DC-side system, and meet the requirements of MMGC performance evaluation, harmonic analysis and circuit parameter design.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] A time-domain steady-state analysis method for islanded operation of a network-type modular multilevel converter (MMGC) can fully meet the requirements for MMGC performance evaluation, harmonic analysis, and circuit parameter design. Its key features include: considering the coupling between the passive network, MMGC, and DC-side system, as well as the coupling relationships of various electrical quantities within the MMGC, to establish a time-domain steady-state analysis model; this model can directly obtain the amplitude and phase angle of each electrical quantity, facilitating performance evaluation and harmonic analysis; and based on the established time-domain steady-state analysis model, it provides a basis for MMGC circuit parameter design.

[0008] The islanded operation domain analysis method for grid-type modular multilevel converters is implemented according to the following steps:

[0009] Step 1: Constructing the AC and DC equivalent circuits of the MMGC topology during islanded operation;

[0010] The second step is to construct a time-domain steady-state analysis model for MMGC that considers coupling relationships.

[0011] The third step is to study the influence of the LC filter on the capacitor voltage of the submodule.

[0012] The construction of the AC and DC equivalent circuits for the first step of islanded operation of MMGC is implemented according to the following steps:

[0013] 1) For phase A, the current i of the filter inductor Lf,a (t) is:

[0014] i Lf,a (t)=i s,a (t)+i Cf,a (t) (1)

[0015] Among them, i Cf,a (t) is the current in the filter capacitor, i s,a (t) is the phase current output to the passive network;

[0016] i s,a (t) is represented as:

[0017] i s,a (t)=I s cos(wt+β s (2)

[0018] Among them, I s and β s These are the amplitude and phase angle of the phase current, respectively, and w is the fundamental angular frequency;

[0019] Because the MMGC is connected to a passive network and operates in constant voltage mode, the voltage u of the filter capacitor... Cf,a (t) is represented as:

[0020] u Cf,a(t)=U Cf cos(wt) (3)

[0021] Among them, U Cf It is the amplitude of the voltage across the filter capacitor;

[0022] 2) The arm current of MMGC is expressed as:

[0023]

[0024] Among them, i ap (t) and i an (t) represent the currents of the upper and lower bridge arms, respectively, i cir,a (t) represents circulation;

[0025] 3) According to KVL law, the voltage relationship between the upper and lower bridge arms is expressed as:

[0026]

[0027]

[0028] Among them, u ap (t) and u an (t) represents the voltage of the upper and lower bridge arms, respectively, R m and L m L represents the bridge arm resistance and bridge arm inductance, respectively. f U represents the AC side inductance. dc Indicates the DC side voltage;

[0029] Subtracting and adding equations (5) and (6) respectively, we obtain the equations for the AC side and DC side as follows:

[0030]

[0031]

[0032] Among them, u equ,ac (t) and u equ,dc (t) represents the equivalent electromotive force on the AC side and the DC side, respectively; Equations (7) and (8) are the AC and DC equivalent circuits of the MMGC topology when running in an islanded environment, respectively.

[0033] The second step, constructing the MMGC time-domain steady-state analysis model considering coupling relationships, is implemented according to the following steps:

[0034] 1) The fundamental component of the modulation signal is used for the power output of the MMGC, and the second harmonic component is used to suppress the second harmonic circulating current. The modulation signal is written as:

[0035]

[0036] Among them, Sap (t) and S an (t) represents the modulation signals of the upper and lower bridge arms, A1 and A2 represent the amplitudes of the fundamental frequency and second harmonic components of the modulation signals, and α1 and α2 represent the initial phase angles corresponding to the fundamental frequency and second harmonic of the modulation signals, respectively.

[0037] 2) The capacitor voltage of the submodule in the upper and lower bridge arms is expressed as follows:

[0038]

[0039] Among them, u cap,ap (t) and u cap,an (t) represents the capacitor voltage of the upper and lower bridge arm submodules, respectively. M It is the capacitance value of the submodule, U c,dc It is the DC component of the capacitor voltage;

[0040] 3) The output voltage of the submodules in the upper and lower bridge arms is equal to the product of the capacitor voltage and the modulation signal. Assuming that after applying the submodule capacitor voltage balancing strategy, the N submodules in each bridge arm have the same voltage value, the voltages of the upper and lower bridge arms are calculated as follows:

[0041]

[0042] 4) Solve the four unknowns A1 and A2, α1 and α2 using equations (1) to (11), and the results are shown in equations (12) to (17);

[0043]

[0044]

[0045] Among them, M1 to M4 are intermediate variables used to simplify the expression of A1 and α1, and their expressions are shown in equation (13).

[0046]

[0047]

[0048]

[0049]

[0050] Among them, N1 to N4 are intermediate variables used to simplify the expression of A2 and α2, and their expressions are shown in equation (17).

[0051]

[0052] 5) In equations (12)-(17), the DC current I dc By expressing it as equation (18)

[0053]

[0054] Based on equations (2), (4), (5), (6), (9), (10), and (18), a steady-state analysis model of the MMGC time domain is established, which can obtain the DC side current I. dc AC side current i s,a (t), upper and lower bridge arm modulation signals S ap (t) and S an (t), upper and lower bridge arm currents i ap (t) and i an (t), upper and lower bridge arm voltages u ap (t) and u an (t), the capacitor voltage u of the submodule in the upper and lower bridge arms cap,ap (t) and u cap,an The magnitude and phase angle of (t).

[0055] The study of the impact of the LC filter on the submodule capacitor voltage in the third step is implemented in the following steps:

[0056] 1) The research process mainly focuses on the following two aspects: the fluctuation of the submodule capacitor voltage u c,flu and the peak value of capacitor voltage U c,peak ;

[0057] Based on the established MMGC time-domain analysis model, it is found that the filter capacitor has a significant impact on the fluctuation and peak value of the submodule capacitor voltage; while the filter inductor has negligible impact on the fluctuation and peak value of the submodule capacitor voltage.

[0058] 2) When the AC load is mainly composed of inductive load, the value of the filter capacitor should be smaller than that when the AC load is mainly composed of resistive load.

[0059] 3)u c,flu The maximum value occurs when MMGC provides a purely inductive load; U c,peak The maximum value occurs when the MMGC provides a purely resistive load;

[0060] 4) Since the actual load consists of resistors and inductors, therefore u c,flu and U c,peak All of these must be monitored to ensure that the capacitor voltage does not exceed its limit throughout the entire operating range of the converter.

[0061] This invention presents a time-domain steady-state analysis method for islanded operation of a modular multilevel converter (MMGC). This method fully meets the requirements for MMGC performance evaluation, harmonic analysis, and circuit parameter design. It analyzes the coupling between the passive network, MMGC, and DC-side system, as well as the coupling relationships of various electrical quantities within the MMGC, and establishes a time-domain steady-state analysis model. This model, established in the time domain, directly yields the amplitude and phase angle of each electrical quantity, facilitating performance evaluation and harmonic analysis. Based on the established model, it is concluded that the submodule capacitors are highly correlated with the filter capacitors but almost uncorrelated with the filter inductors, and that the selection of filter capacitors must consider load characteristics, providing a basis for MMGC circuit parameter design. The established time-domain analysis model exhibits high accuracy under various operating conditions and can replace time-consuming EMT simulations.

[0062] Compared with existing methods, the beneficial effects of the present invention are:

[0063] 1) A time-domain steady-state analysis model for the MMGC was established, which can fully reflect the coupling relationship between the load, the MMGC, and the DC-side system. Based on this model, all electrical quantities of the MMGC can be easily calculated.

[0064] 2) Since the model is established in the time domain, the amplitude and phase angle of each harmonic component of the electrical quantity can be obtained directly, which is very convenient for performance evaluation and harmonic analysis.

[0065] 3) Based on the established model, it is concluded that the submodule capacitor is highly correlated with the filter capacitor, but almost uncorrelated with the filter inductor, and that the selection of the filter capacitor should take into account the load characteristics. This model can be used for circuit parameter design. The model has high accuracy under various operating conditions and can replace time-consuming EMT simulation. Attached Figure Description

[0066] Figure 1 This is a typical circuit topology for a three-phase MMGC operating in an islanded environment;

[0067] Figure 2 Equivalent circuit diagrams for MMGC AC and DC;

[0068] Figure 3 A diagram showing the coupling relationships of various electrical quantities in MMGC;

[0069] Figure 4 Flowchart for solving the time-domain steady-state expressions of various electrical quantities in MMGC. Detailed Implementation

[0070] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0071] This invention discloses a method for islanded operation domain analysis of a grid-type modular multilevel converter (MMGC). A typical circuit topology for a three-phase MMGC operating in islanded mode is shown below. Figure 1 As shown, the MMGC consists of three phases, with two bridge arms per phase. Each bridge arm has N series-connected half-bridge sub-modules and a bridge arm inductor L. m The system consists of an LC filter installed on the AC side to reduce switching harmonics. The time-domain analysis model is established as follows.

[0072] The islanded operation domain analysis method for grid-type modular multilevel converters is implemented according to the following steps:

[0073] Step 1: Constructing AC and DC equivalent circuits for the MMGC topology during islanded operation

[0074] The first step of constructing the AC / DC equivalent circuit is carried out in the following steps:

[0075] 1) Taking phase A as an example, the current i of the filter inductor Lf,a (t) is:

[0076] i Lf,a (t)=i s,a (t)+i Cf,a (t) (1)

[0077] Among them, i Cf,a (t) is the current in the filter capacitor, i s,a (t) is the phase current output to the passive network.

[0078] i s,a (t) can be represented as:

[0079] i s,a (t)=I s cos(wt+β s (2)

[0080] Among them, I s and β s These are the amplitude and phase angle of the phase current, respectively, and w is the fundamental angular frequency.

[0081] Because the MMGC is connected to a passive network and operates in constant voltage mode, the voltage u of the filter capacitor... Cf,a (t) can be expressed as:

[0082] u Cf,a (t)=U Cf cos(wt) (3)

[0083] Among them, U Cf It is the amplitude of the voltage across the filter capacitor.

[0084] 2) The arm current of MMGC is expressed as:

[0085]

[0086] Among them, i ap (t) and i an (t) represent the currents of the upper and lower bridge arms, respectively, i cir,a (t) represents circulation.

[0087] 3) According to KVL law, the voltage relationship between the upper and lower bridge arms is expressed as:

[0088]

[0089]

[0090] Among them, u ap (t) and u an (t) represents the voltage of the upper and lower bridge arms, respectively, R m and L m L represents the bridge arm resistance and bridge arm inductance, respectively. f U represents the AC side inductance. dc This indicates the DC side voltage.

[0091] Subtracting and adding equations (5) and (6) respectively, we obtain the equations for the AC side and DC side as follows:

[0092]

[0093]

[0094] Among them, u equ,ac (t) and u equ,dc (t) represents the equivalent electromotive force on the AC side and the DC side, respectively.

[0095] Equations (7) and (8) are the AC and DC equivalent circuits of the MMGC topology when running in an islanded environment, respectively.

[0096] MMGC AC and DC equivalent circuit diagrams are as follows Figure 2 As shown, this circuit diagram reflects the coupling relationship between the passive network, MMGC, and DC-side system.

[0097] Step 2: Constructing a time-domain steady-state analysis model for MMGC considering coupling relationships.

[0098] and Figure 2 The coupling between external electrical quantities is similar; the coupling relationship diagram of the electrical quantities inside the MMGC is as follows: Figure 3 As shown.

[0099] The second step, constructing the time-domain steady-state analysis model, is implemented according to the following steps:

[0100] 1) The fundamental component of the modulation signal is used for the power output of the MMGC, and the second harmonic component is used to suppress the second harmonic circulating current. The modulation signal can be written as:

[0101]

[0102] Among them, S ap (t) and S an (t) represents the modulation signals of the upper and lower bridge arms, A1 and A2 represent the amplitudes of the fundamental frequency and second harmonic components of the modulation signals, and α1 and α2 represent the initial phase angles corresponding to the fundamental frequency and second harmonic components of the modulation signals, respectively.

[0103] 2) The capacitor voltage of the submodule in the upper and lower bridge arms is expressed as follows:

[0104]

[0105] Among them, u cap,ap (t) and u cap,an (t) represents the capacitor voltage of the upper and lower bridge arm submodules, respectively. M It is the capacitance value of the submodule, U c,dc It is the DC component of the capacitor voltage.

[0106] 3) The output voltage of the submodules in the upper and lower bridge arms is equal to the product of the capacitor voltage and the modulation signal. Assuming that after applying the submodule capacitor voltage balancing strategy, the N submodules in each bridge arm have the same voltage value, the voltages of the upper and lower bridge arms can be calculated as follows:

[0107]

[0108] 4) The four unknowns A1 and A2, α1 and α2 can be solved by equations (1) to (11), and the results are shown in equations (12) to (17).

[0109]

[0110]

[0111] The expressions for M1-M4 are shown in equation (13).

[0112]

[0113]

[0114]

[0115]

[0116] The expressions for N1-N4 are shown in equation (17).

[0117]

[0118] 5) In equations (12)-(17), the DC current I dc This can be expressed as equation (18).

[0119]

[0120] Use Z load and Let represent the impedance magnitude and phase angle of the passive network respectively. The phase current magnitude and phase angle in equations (12)-(17) can be expressed as equation (19).

[0121]

[0122] Based on equations (2), (4), (5), (6), (9), (10), and (18), a steady-state analysis model of the MMGC time domain is established, which can obtain the DC side current I. dc AC side current i s,a (t), upper and lower bridge arm modulation signals S ap (t) and S an (t), upper and lower bridge arm currents i ap (t) and i an (t), upper and lower bridge arm voltages u ap (t) and u an (t), the capacitor voltage u of the submodule in the upper and lower bridge arms cap,ap (t) and u cap,an The amplitude and phase angle of (t). The flowchart for solving the time-domain steady-state expressions of various electrical quantities in MMGC is shown below. Figure 4 As shown, based on the established time-domain analysis model, all electrical quantities of MMGC can be easily calculated.

[0123] Step 3: Study on the influence of the LC filter on the capacitor voltage of the submodule

[0124] The third step, the study of the filter's effect on capacitor voltage, is implemented according to the following steps:

[0125] 1) The research process mainly focuses on the following two aspects: the fluctuation of the submodule capacitor voltage u c,flu and the peak value of capacitor voltage U c,peak .

[0126] Based on the established MMGC time-domain analysis model, it can be concluded that the filter capacitor has a significant impact on the fluctuation and peak value of the submodule capacitor voltage; while the effect of the filter inductor on the fluctuation and peak value of the submodule capacitor voltage is negligible.

[0127] 2) When the AC load is mainly composed of inductive load, the value of the filter capacitor should be smaller than that when the AC load is mainly composed of resistive load.

[0128] 3)u c,fluThe maximum value occurs when MMGC provides a purely inductive load; U c,peak The maximum value occurs when MMGC provides a purely resistive load.

[0129] 4) Since actual loads are usually composed of resistors and inductors, u c,flu and U c,peak All of these must be monitored to ensure that the capacitor voltage does not exceed its limit throughout the entire operating range of the converter.

Claims

1. A method for islanded operation domain analysis of network-type modular multilevel converters, which can fully meet the requirements of MMGC performance evaluation, harmonic analysis, and circuit parameter design, is characterized by: Considering the coupling of the passive network, MMGC and DC-side system, as well as the coupling relationship of various electrical quantities within the MMGC, a time-domain steady-state analysis model is established. This model can directly obtain the amplitude and phase angle of each electrical quantity, which is convenient for performance evaluation and harmonic analysis. Based on the established time-domain steady-state analysis model, a basis is provided for the design of MMGC circuit parameters. The islanded operation domain analysis method for grid-type modular multilevel converters is implemented according to the following steps: Step 1: Constructing the AC and DC equivalent circuits of the MMGC topology during islanded operation; The second step is to construct a time-domain steady-state analysis model for MMGC that considers coupling relationships. The third step is to study the influence of the LC filter on the capacitor voltage of the submodule. The second step, constructing the MMGC time-domain steady-state analysis model considering coupling relationships, is implemented according to the following steps: 1) The fundamental component of the modulation signal is used for the power output of the MMGC, and the second harmonic component is used to suppress the second harmonic circulating current. The modulation signal is written as: (9) in, and These are the modulation signals for the upper and lower bridge arms, respectively. and These are the amplitudes of the fundamental frequency and the second harmonic component of the modulation signal, respectively. and These are the initial phase angles corresponding to the fundamental frequency and second harmonic of the modulation signal, respectively; 2) The capacitor voltage of the submodule in the upper and lower bridge arms is expressed as follows: (10) in, and These represent the capacitor voltages of the upper and lower bridge arm submodules, respectively. It is the capacitance value of the submodule. It is the DC component of the capacitor voltage; 3) The output voltage of the submodule in the upper and lower bridge arms is equal to the product of the capacitor voltage and the modulation signal. Assuming that after applying the submodule capacitor voltage balancing strategy, the output voltage of each bridge arm... N Each submodule has the same voltage value; the voltage of the upper and lower bridge arms is calculated as follows: (11) 4) Solve for and , and The results for these four unknowns are shown in equations (12)-(17); (12) (13) in, It is for simplification and The intermediate variable is expressed as shown in equation (13); (14a) (14b) (15) (16) in, It is for simplification and The intermediate variable is expressed as shown in equation (17); (17) 5) DC current in equations (12)-(17) By expressing it as equation (18) (18) By establishing a time-domain steady-state analysis model of MMGC, the DC-side current can be obtained. AC side current upper and lower bridge arm modulation signals and Upper and lower bridge arm currents and Upper and lower bridge arm voltages and The capacitor voltage of the submodule in the upper and lower bridge arms and The amplitude and phase angle.

2. The islanded operation domain analysis method for a grid-type modular multilevel converter according to claim 1, characterized in that: The construction of the AC and DC equivalent circuits for the first step of islanded operation of MMGC is implemented according to the following steps: 1) For phase A, the current in the filter inductor for: (1) in, It is the current of the filter capacitor. It is the phase current output to the passive network; Represented as: (2) in, and These are the amplitude and phase angle of the phase current, respectively. The fundamental angular frequency; Because the MMGC is connected to a passive network, it operates in constant voltage mode, and the voltage of the filter capacitor... Represented as: (3) in, It is the amplitude of the voltage across the filter capacitor; 2) The bridge arm current of MMGC is expressed as: (4) in, and These represent the currents of the upper and lower bridge arms, respectively. Indicates circulation; 3) According to KVL law, the voltage relationship between the upper and lower bridge arms is expressed as: (5) (6) in, and These represent the voltages of the upper and lower bridge arms, respectively. and These represent the bridge arm resistance and bridge arm inductance, respectively. Indicates the AC side inductance. Indicates the DC side voltage; Subtracting and adding equations (5) and (6) respectively, we obtain the equations for the AC side and DC side as follows: (7) (8) in, and These are the equivalent electromotive forces on the AC and DC sides, respectively; Equations (7) and (8) are the AC and DC equivalent circuits of the MMGC topology during islanded operation, respectively.

3. The islanded operation domain analysis method for a grid-type modular multilevel converter according to claim 1, characterized in that: The study of the impact of the LC filter on the submodule capacitor voltage in the third step is implemented in the following steps: 1) The research process mainly focuses on the following two aspects: fluctuations in the capacitor voltage of the submodule. and the peak value of capacitor voltage ; Based on the established MMGC time-domain analysis model, it is found that the filter capacitor has a significant impact on the fluctuation and peak value of the submodule capacitor voltage; while the filter inductor has negligible impact on the fluctuation and peak value of the submodule capacitor voltage. 2) When the AC load is mainly composed of inductive load, the value of the filter capacitor should be smaller than that when the AC load is mainly composed of resistive load. 3) The maximum value occurs when MMGC provides purely inductive load; The maximum value occurs when the MMGC provides a purely resistive load; 4) Since the actual load consists of resistors and inductors, therefore and All of these must be monitored to ensure that the capacitor voltage does not exceed its limit throughout the entire operating range of the converter.

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