A fault ride-through control method and control circuit for a flexible low-frequency power transmission system

By addressing the challenges in flexible low-frequency power transmission systems, detecting fault types, and implementing dynamic fault control for inverter and rectifier-side converters, a voltage and current control loop model was constructed. This enabled dynamic performance adjustment during faults, improving system stability and efficiency.

CN119093471BActive Publication Date: 2025-11-18CHINA ENERGY ENG GRP GUANGDONG ELECTRIC POWER DESIGN INST CO LTD
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Patent Information

Application Number
CN202411101209.7
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2024-08-12
Publication Date
2025-11-18
Estimated Expiration
2044-08-12

AI Technical Summary

Technical Problem

Existing flexible low-frequency power transmission systems cannot adjust their dynamic performance in a timely manner during faults, affecting system efficiency.

Method used

By detecting the fault type, dynamic fault control is performed on the inverter-side and rectifier-side converters respectively. The output voltage reference value of the inverter-side converter is calculated using the DC bus voltage, and the rectifier-side converter is controlled according to the system operating characteristics. A voltage and current control loop model is constructed to achieve dynamic adjustment during faults.

Benefits of technology

It enables dynamic performance adjustment of the flexible low-frequency power transmission system during faults, ensuring normal system operation, improving system stability and efficiency, and protecting against equipment failure risks.

✦ Generated by Eureka AI based on patent content.

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Patent Text Reader

Abstract

The application discloses a kind of flexible low-frequency power transmission system's fault ride-through control method and control circuit, by setting up full-bridge type distributed pressure relief device in the flexible low-frequency converter station inverter side construction power frequency ac fault ride-through controller, and according to the operating characteristics of flexible low-frequency converter station rectifier side system under low-frequency ac fault, low-frequency ac fault ride-through controller is constructed, to design flexible low-frequency converter station cooperative fault ride-through control method according to power frequency ac fault ride-through controller and low-frequency ac fault ride-through controller, and according to the flexible low-frequency converter station cooperative fault ride-through control method, control parameter optimization is carried out, to adjust the dynamic performance of system during the failure of flexible low-frequency power transmission system in time, avoid affecting system efficiency, so that system normal operation.
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Description

Technical Field

[0001] This invention relates to the field of new energy grid-connected power generation technology, and in particular to a fault ride-through control method and control circuit for a flexible low-frequency power transmission system. Background Technology

[0002] Flexible low-frequency (LHF) transmission systems eliminate the need for bulky and heavy sending-end converter stations, effectively reducing the construction and operation costs of transmission systems and becoming a highly competitive renewable energy transmission solution. This solution utilizes a lower operating frequency in the low-frequency AC system, offering significant advantages in reducing line losses, charging current, and reactive current. Therefore, flexible LHF transmission systems have a stronger power transmission capacity compared to traditional high-voltage AC transmission systems. Furthermore, equipment such as AC circuit breakers in flexible LHF transmission systems can draw upon existing mature technologies from high-voltage AC transmission system engineering, which will help promote the research and application of flexible LHF transmission systems.

[0003] Flexible low-frequency converter stations are the core components of flexible low-frequency transmission systems, which differ significantly from high-voltage AC transmission systems. Therefore, the dynamic performance of flexible low-frequency transmission systems also differs considerably from that of traditional high-voltage AC systems. Flexible low-frequency converter stations are susceptible to low-frequency AC faults and power frequency AC faults, which can cause them to deviate from normal operating conditions and pose a significant threat to the safe and stable operation of the flexible low-frequency transmission system.

[0004] Existing fault control methods for flexible low-frequency transmission systems mainly focus on the steady-state control performance of the system, while paying less attention to the dynamic performance of the system during faults. This makes it impossible to adjust the dynamic performance of the system in a timely manner during faults, which affects the system's operating efficiency. Summary of the Invention

[0005] This invention provides a fault ride-through control method and control circuit for a flexible low-frequency power transmission system, in order to solve the problem that existing flexible low-frequency power transmission systems cannot adjust the dynamic performance of the system in a timely manner during faults, thus affecting the system's operating efficiency.

[0006] To address the aforementioned technical problems, embodiments of the present invention provide a fault ride-through control method for a flexible low-frequency power transmission system, comprising:

[0007] Detecting fault types in the power transmission system, including power frequency AC faults and low frequency AC faults;

[0008] If the fault type is a power frequency AC fault, the first output voltage reference value of the inverter-side converter is calculated based on the DC bus voltage, and the inverter-side converter of the flexible low-frequency converter station is subjected to fault control based on the first output voltage reference value.

[0009] If the fault type is a low-frequency AC fault, then the rectifier-side converter of the flexible low-frequency converter station is subjected to fault control according to the operating characteristics of the rectifier-side system of the flexible low-frequency converter station.

[0010] This invention monitors the fault types of the power transmission system in real time, and then performs dynamic fault control on the inverter-side converters of the flexible low-frequency converter station according to the fault types of the power transmission system. This allows for timely adjustment of the dynamic performance of the system during fault periods, avoiding impact on system efficiency and ensuring normal system operation.

[0011] Furthermore, the step of calculating the first output voltage reference value of the inverter-side converter based on the DC bus voltage, and performing fault control on the inverter-side converter of the flexible low-frequency converter station based on the first output voltage reference value, specifically involves:

[0012] Calculate the steady-state reference value of the first output voltage based on the error between the DC bus voltage and the maximum DC bus voltage.

[0013] Calculate the first voltage compensation value, and calculate the first output voltage reference value of the inverter-side converter based on the first voltage compensation value and the first voltage output reference value;

[0014] Fault control is performed on the inverter-side converter of the flexible low-frequency converter station based on the first output voltage reference value.

[0015] The first steady-state reference value of the output voltage is as follows:

[0016] U FBf =k pFB (U dc -U dcmax )+k iFB ∫(U dc -U dcmax )

[0017] Where, k pFB and k iFB These are the proportional and integral coefficients of the power frequency AC fault ride-through control module; U dcmax This represents the maximum DC bus voltage of the flexible low-frequency converter station.

[0018] The first voltage compensation value is specifically:

[0019] Δu FB =k pFBΔ (U FBΔ -U FBsmN )+k iFBΔ ∫(U FBΔ -U FBsmN )

[0020] Where, kpFBΔ and k iFBΔ These are the proportional coefficient and integral coefficient of the power frequency AC fault ride-through control module, respectively.

[0021] Furthermore, the fault control of the rectifier-side converter of the flexible low-frequency converter station based on the operating characteristics of the rectifier-side system specifically includes:

[0022] The current low-frequency AC current is detected. If the low-frequency AC current is less than or equal to a preset current threshold, the second output voltage reference value of the rectifier-side converter is calculated according to the first control module, and the inverter-side converter is subjected to fault control according to the second output voltage reference value. The first control module is constructed based on the voltage control loop transmission model of the low-frequency AC voltage.

[0023] If the low-frequency AC current is greater than the preset current threshold, the first output current reference value of the rectifier-side converter is calculated according to the second control module, and the inverter-side converter is subjected to fault control according to the first output current reference value; the second control module is constructed based on the system operating characteristics of the rectifier-side converter.

[0024] Furthermore, based on the energy transfer model of the power frequency AC power grid, an equivalent circuit model of the flexible low-frequency power transmission system is constructed;

[0025] Based on the equivalent circuit model of the flexible low-frequency power transmission system, a voltage control loop model of the rectifier-side converter is constructed.

[0026] A first control module is constructed based on the voltage control loop transfer model of the low-frequency AC voltage. Specifically, the first control module comprises:

[0027]

[0028] in, and These are the reference values ​​for the AC side d-axis voltage and q-axis voltage of the rectifier-side converter in the flexible low-frequency converter station; u d and u q These are the actual values ​​of the AC side d-axis voltage and q-axis voltage of the rectifier-side converter in the flexible low-frequency converter station; G iLFAC (s) is the transfer function of the current control loop controller; ω LFAC For the frequency of flexible low-frequency power transmission systems; i LFACd and i LFACq These represent the actual d-axis and q-axis current values ​​of the low-frequency AC line in a flexible low-frequency transmission system; L LFAC Inductance for low-frequency AC lines in a flexible low-frequency transmission system;

[0029] The second output voltage reference value is calculated based on the first control module. The second output voltage reference value includes a direct-axis voltage reference value and a quadrature-axis voltage reference value.

[0030] Furthermore, the calculation of the first output current reference value of the rectifier-side converter based on the second control module specifically involves:

[0031] Based on the energy transfer model of the power frequency AC power grid, an equivalent circuit model of the flexible low-frequency power transmission system is constructed.

[0032] A second control module is constructed based on the equivalent circuit model of the flexible low-frequency power transmission system and the maximum output current of the rectifier-side converter of the flexible low-frequency converter station. Specifically, the second control module is as follows:

[0033]

[0034] Among them, i LFACmax k represents the maximum output current of the rectifier-side converter in the flexible low-frequency converter station. pmax and k imax For the proportional and integral coefficients of the low-frequency AC fault ride-through control loop controller based on the maximum and minimum current; The voltage threshold for switching the system to a low-frequency AC fault-crossing control loop based on maximum and minimum current; For low-frequency AC system voltage amplitude; i LFACN This refers to the rated output current of the rectifier-side converter in the flexible low-frequency converter station.

[0035] The second control module calculates a first output current reference value for the low-frequency AC line, which includes a direct-axis current reference value and a quadrature-axis current reference value.

[0036] Fault control is performed on the rectifier-side converter of the flexible low-frequency converter station based on the second output voltage reference value.

[0037] Secondly, the present invention provides a fault ride-through control circuit for a flexible low-frequency power transmission system, used to implement the fault ride-through control method of the power transmission system, including: a power frequency AC fault ride-through control module, a low-frequency AC fault ride-through control module, a flexible low-frequency converter station, a low-frequency AC power grid, and a power frequency AC power grid;

[0038] The flexible low-frequency converter station includes a rectifier-side converter and an inverter-side converter; the rectifier-side converter is connected to the low-frequency AC power grid; the inverter-side converter is connected to the power frequency AC power grid.

[0039] The input terminal of the power frequency AC fault ride-through control module is connected to the power frequency AC power grid, and the output terminal of the power frequency AC fault ride-through control module is connected to the inverter-side converter; the input terminal of the low frequency AC fault ride-through control module is connected to the low frequency AC power grid, and the output terminal of the low frequency AC fault ride-through control module is connected to the rectifier-side converter.

[0040] Furthermore, the power frequency AC fault ride-through control module includes: an output voltage steady-state control module, an output voltage compensation control module, and a first voltage modulation module;

[0041] The output terminal of the first voltage modulation module is connected to the inverter-side converter, and the input terminal of the first voltage modulation module is connected to the output voltage steady-state control module and the output voltage compensation control module. The first voltage modulation module is used to perform fault control on the inverter-side converter.

[0042] The output voltage steady-state control module includes a full-bridge submodule group, a bleed resistor, and a smoothing capacitor. The full-bridge submodule group includes several full-bridge submodules connected in series. The full-bridge submodule group and the bleed resistor are connected in series to form an energy discharge path. The energy discharge path and the smoothing capacitor are connected in parallel.

[0043] Furthermore, the output voltage steady-state control module includes a full-bridge submodule group, a bleed resistor, and a smoothing capacitor;

[0044] The full-bridge submodule group includes several full-bridge submodules connected in series. The full-bridge submodule group and the discharge resistor are connected in series to form an energy discharge path. The energy discharge path is connected in parallel with the smoothing capacitor.

[0045] Furthermore, the equivalent circuit model of the output voltage steady-state control module is as follows:

[0046]

[0047] Among them, U FB U is the output voltage of the full-bridge submodule group. dc Represents the DC bus voltage of the flexible low-frequency converter station; C f For smoothing capacitor, R f For bleed resistor;

[0048] The output voltage of the full-bridge submodule group is specifically as follows:

[0049]

[0050] Where t∈[0,T] Cf ], T Cf U represents the charge / discharge cycle of the full-bridge submodule capacitor;FBmax U represents the maximum output voltage of the full-bridge submodule group. FBmin This is the minimum output voltage of the full-bridge submodule group.

[0051] Furthermore, the fault ride-through control circuit of the power transmission system also includes a parameter optimization module, which is connected to the power frequency AC fault ride-through control module and the low frequency AC fault ride-through control module respectively.

[0052] The parameter optimization module is used to extract feature vectors of all control modules in the power frequency AC fault ride-through control module and the low frequency AC fault ride-through control module, and to optimize and update the proportional coefficient and integral coefficient of each control module based on the feature vectors. Attached Figure Description

[0053] Figure 1 A schematic diagram of a fault ride-through control circuit for a flexible low-frequency power transmission system provided in an embodiment of the present invention;

[0054] Figure 2 This is a schematic diagram of a power frequency AC fault ride-through control module provided in an embodiment of the present invention;

[0055] Figure 3 This is a schematic diagram of a low-frequency AC fault ride-through control module provided in an embodiment of the present invention.

[0056] Figure 4 A flowchart illustrating a fault ride-through control method for a flexible low-frequency power transmission system provided in an embodiment of the present invention;

[0057] Figure 5 A waveform diagram of a fault ride-through control method for a flexible low-frequency power transmission system provided in an embodiment of the present invention;

[0058] Figure 6 Another waveform diagram of a fault ride-through control method for a flexible low-frequency power transmission system provided in an embodiment of the present invention. Detailed Implementation

[0059] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0060] Example 1

[0061] Please refer to Figure 1 , Figure 1A schematic diagram of a fault ride-through control circuit for a flexible low-frequency power transmission system provided in an embodiment of the present invention includes: a power frequency AC fault ride-through control module, a low-frequency AC fault ride-through control module, a flexible low-frequency converter station, a low-frequency AC power grid, and a power frequency AC power grid;

[0062] The flexible low-frequency converter station includes a rectifier-side converter and an inverter-side converter; the rectifier-side converter is connected to the low-frequency AC power grid; the inverter-side converter is connected to the power frequency AC power grid.

[0063] The input terminal of the power frequency AC fault ride-through control module is connected to the power frequency AC power grid, and the output terminal of the power frequency AC fault ride-through control module is connected to the inverter-side converter.

[0064] The input terminal of the low-frequency AC fault ride-through control module is connected to the low-frequency AC power grid, and the output terminal of the low-frequency AC fault ride-through control module is connected to the rectifier-side converter.

[0065] Please refer to Figure 2 , Figure 2 This is a schematic diagram of a power frequency AC fault ride-through control module provided in an embodiment of the present invention.

[0066] In this embodiment, the power frequency AC fault ride-through control module includes: an output voltage steady-state control module, an output voltage compensation control module, and a first voltage modulation module;

[0067] The output terminal of the first voltage modulation module is connected to the inverter-side converter, and the input terminal of the first voltage modulation module is connected to the output voltage steady-state control module and the output voltage compensation control module. The first voltage modulation module is used to perform fault control on the inverter-side converter.

[0068] In this embodiment, the output voltage steady-state control module includes a full-bridge submodule group, a bleed resistor, and a smoothing capacitor;

[0069] The full-bridge submodule group includes several full-bridge submodules connected in series. The full-bridge submodule group and the discharge resistor are connected in series to form an energy discharge path. The energy discharge path is connected in parallel with the smoothing capacitor.

[0070] In this embodiment, when the power frequency AC grid voltage of the flexible low-frequency transmission system changes, the DC bus voltage of the flexible low-frequency converter station changes accordingly. This real-time DC bus voltage is input into the power frequency AC fault ride-through control module. The output voltage steady-state control module outputs a reference value for the output voltage of the full-bridge submodule group of the power frequency AC fault ride-through control module based on the error between the DC bus voltage of the flexible low-frequency converter station and its maximum value. Simultaneously, the expected voltage value of a single submodule in the full-bridge submodule group is calculated based on the average voltage expression of the full-bridge submodules, and then the output voltage compensation of the full-bridge submodule group is obtained according to the output voltage compensation control module.

[0071] In this embodiment, the steady-state reference value of the output voltage of the full-bridge submodule group in the power frequency AC fault ride-through control module is added to the output voltage compensation of the full-bridge submodule group to obtain the first output voltage reference value of the full-bridge submodule group of the power frequency AC fault ride-through control module. The full-bridge submodule group of the power frequency AC fault ride-through control module is modulated according to the first output voltage reference value to realize power frequency AC fault ride-through control.

[0072] Please refer to Figure 3 , Figure 3 This is a schematic diagram of a low-frequency AC fault ride-through control module provided in an embodiment of the present invention.

[0073] In this embodiment, the low-frequency AC fault ride-through control module includes a first control module, a second control module, and a second voltage modulation module, wherein the first control module and the second control module are respectively connected to the second voltage modulation module.

[0074] In this embodiment, when the low-frequency AC grid voltage of the flexible low-frequency transmission system changes, the low-frequency AC bus voltage of the rectifier-side converter of the flexible low-frequency converter station is input to the first control module. The first control module outputs the q-axis current reference value of the low-frequency AC line in the flexible low-frequency transmission system based on the error between the voltage threshold at which the system switches to the first control module and the voltage amplitude of the low-frequency AC system, combined with the rated output current of the rectifier-side converter of the flexible low-frequency converter station. This q-axis current reference value is then calculated by combining the q-axis current reference value with the maximum output current of the rectifier-side converter of the flexible low-frequency converter station.

[0075] In this embodiment, the first control module outputs the AC-side d-axis voltage reference value of the rectifier-side converter of the flexible low-frequency converter station based on the error between the d-axis current reference value and the actual d-axis current value of the low-frequency AC line in the flexible low-frequency transmission system, and the actual q-axis current value of the low-frequency AC line in the flexible low-frequency transmission system; the current control loop of the rectifier-side converter of the flexible low-frequency converter station outputs the AC-side q-axis voltage reference value of the rectifier-side converter of the flexible low-frequency converter station based on the error between the q-axis current reference value and the actual q-axis current value of the low-frequency AC line in the flexible low-frequency transmission system, and the actual d-axis current value of the low-frequency AC line in the flexible low-frequency transmission system.

[0076] In this embodiment, the AC-side d-axis voltage reference values ​​and AC-side q-axis voltage reference values ​​of the rectifier-side converter of the flexible low-frequency converter station are obtained by performing PARK inverse transform and CLARKE inverse transform to obtain the AC-side A-phase voltage reference values, AC-side B-phase voltage reference values, and AC-side C-phase voltage reference values ​​of the rectifier-side converter of the flexible low-frequency converter station. The rectifier-side converter of the flexible low-frequency converter station is modulated based on these AC-side voltage reference values ​​to achieve low-frequency AC fault ride-through control based on maximum and minimum currents.

[0077] In this embodiment, the fault ride-through control method of the power transmission system is implemented according to the fault ride-through control circuit of the power transmission system.

[0078] Please refer to Figure 4 , Figure 4 A flowchart illustrating a fault ride-through control method for a flexible low-frequency transmission system provided in an embodiment of the present invention is shown below:

[0079] Detecting fault types in the power transmission system, including power frequency AC faults and low frequency AC faults;

[0080] If the fault type is a power frequency AC fault, the first output voltage reference value of the inverter-side converter is calculated based on the DC bus voltage, and the inverter-side converter of the flexible low-frequency converter station is subjected to fault control based on the first output voltage reference value.

[0081] If the fault type is a low-frequency AC fault, then the rectifier-side converter of the flexible low-frequency converter station is subjected to fault control according to the operating characteristics of the rectifier-side system of the flexible low-frequency converter station.

[0082] In this embodiment, the output voltage of each full-bridge submodule in the power frequency AC fault ride-through control module has three states: 0, +U, ... FBSM -UFBSM The output voltage of the full-bridge submodule group is controlled to adapt to changes in the DC bus voltage inside the flexible low-frequency converter station, thereby controlling the discharge resistor R during power frequency AC faults. f The voltage and power consumption at both ends, and the smoothing capacitor C f Its main function is to suppress voltage harmonics generated during frequent switching of the full-bridge submodule group. When a power frequency AC fault occurs, the power transmission from the line is obstructed, resulting in surplus power on the DC bus inside the flexible low-frequency converter station. This causes the DC bus voltage to rise, leading to overvoltage in the capacitors of the inverter submodules on the inverter side of the flexible low-frequency converter station. At this time, the full-bridge distributed voltage relief device installed inside the submodule starts to function, preventing overvoltage problems in the submodule through energy discharge paths, thereby maintaining the stable operation of the flexible low-frequency transmission system and reducing the failure risk of the flexible low-frequency converter station components.

[0083] In this embodiment, the step of calculating the first output voltage reference value of the inverter-side converter based on the DC bus voltage, and performing fault control on the inverter-side converter of the flexible low-frequency converter station based on the first output voltage reference value, specifically includes:

[0084] Calculate the steady-state reference value of the first output voltage based on the error between the DC bus voltage and the maximum DC bus voltage.

[0085] Calculate the first voltage compensation value, and calculate the first output voltage reference value of the inverter-side converter based on the first voltage compensation value and the first voltage output reference value;

[0086] Fault control is performed on the inverter-side converter of the flexible low-frequency converter station based on the first output voltage reference value.

[0087] In this embodiment, the output voltage of the full-bridge submodule group in the power frequency AC fault ride-through control module is specifically as follows:

[0088]

[0089] Where t∈[0,T] Cf ], T Cf U represents the charge / discharge cycle of the full-bridge submodule capacitor; FBmax U represents the maximum output voltage of the full-bridge submodule group. FBmin This is the minimum output voltage of the full-bridge submodule group.

[0090] In this embodiment, the output current of the full-bridge submodule group in the power frequency AC fault ride-through control module is specifically as follows:

[0091] I FB = (U FBmax -U FB ) / Rf (2)

[0092] Based on the charging and discharging balance condition of the submodule capacitor within a cycle, the time expressions for each stage within a cycle are obtained:

[0093]

[0094] In this embodiment, the duty cycle is set to D. FB =t3 / T Cf Based on the time expression and output voltage value expression of the full-bridge submodule group within one cycle, the output voltage model of the full-bridge submodule group in the power frequency AC fault ride-through control module is constructed as follows:

[0095]

[0096] In this embodiment, the full-bridge submodule group contains n full-bridge submodules. The equivalent circuit model of the full-bridge distributed pressure relief device is as follows:

[0097]

[0098] Among them, U dc This represents the DC bus voltage of the flexible low-frequency converter station.

[0099] In this embodiment, the duty cycle D is determined based on the output voltage model and equivalent circuit model of the full-bridge submodule group in the full-bridge distributed pressure relief device. FB With the DC bus voltage U of the flexible low-frequency converter station dc The corresponding relationship. Based on the power frequency AC fault ride-through control module and the DC bus voltage U of the flexible low-frequency converter station. dc The steady-state reference value of the output voltage of the full-bridge submodule group is calculated as follows:

[0100] U FBf =k pFB (U dc -U dcmax )+k iFB ∫(U dc -U dcmax (6)

[0101] Where, k pFB and k iFB These are the proportional and integral coefficients of the controller for a full-bridge distributed pressure relief device; U dcmax This represents the maximum DC bus voltage of the flexible low-frequency converter station.

[0102] In this embodiment, the cutoff frequency of the output voltage steady-state control module of the full-bridge submodule group in the power frequency AC fault ride-through control module is set to 1000Hz, thereby accelerating the response speed of the control loop and reducing the adverse effects of high-frequency noise on the output voltage waveform quality and system stability.

[0103] In this embodiment, based on the modular structure of the full-bridge submodule group in the power frequency AC fault ride-through control module, an average voltage model of the full-bridge submodule is constructed, specifically as follows:

[0104]

[0105] Among them, U FBsmN This represents the expected voltage value of a single full-bridge submodule within the full-bridge submodule group.

[0106] In this embodiment, an output voltage compensation control module is constructed based on the average voltage model of the full-bridge submodule of the power frequency AC fault ride-through control module in the flexible low-frequency converter station, specifically as follows:

[0107] Δu FB =k pFBΔ (U FBΔ -U FBsmN )+k iFBΔ ∫(U FBΔ -U FBsmN (8)

[0108] Where, k pFBΔ and k iFBΔ These are the proportional and integral coefficients of the output voltage compensation controller for the full-bridge submodule group, respectively.

[0109] In this embodiment, according to the output voltage compensation control module, when the voltage of the full-bridge submodule capacitor is higher than the expected voltage value, the voltage can be reduced to the expected value; when the voltage of the full-bridge submodule capacitor is lower than the expected voltage value, the voltage can be increased to the expected value, thereby realizing dynamic compensation of the output voltage of the full-bridge submodule group in the full-bridge distributed pressure relief device.

[0110] In this embodiment, the cutoff frequency of the output voltage compensation control module of the full-bridge submodule group in the power frequency AC fault ride-through control module is set to 800Hz, thereby accelerating the response speed of the control loop and reducing the adverse effects of high-frequency noise on the output voltage waveform quality and system stability.

[0111] In this embodiment, the power frequency AC fault ride-through control module of the flexible low-frequency converter station acquires the DC bus voltage and the output voltage of the full-bridge submodule group of the flexible low-frequency converter station in real time. It then inputs these values, along with the preset maximum value of the DC bus voltage of the flexible low-frequency converter station and the expected voltage value of a single full-bridge submodule in the full-bridge submodule group, into the pre-constructed power frequency AC fault ride-through control module. This enables the flexible low-frequency transmission system to suppress the overvoltage phenomenon caused by the obstruction of power transmission on the DC bus voltage of the flexible low-frequency converter station when a voltage drop fault occurs in the power frequency grid, thus ensuring the safe and reliable operation of the flexible low-frequency converter station and improving the stability of the flexible low-frequency transmission system.

[0112] In this embodiment, the fault control of the rectifier-side converter of the flexible low-frequency converter station based on the operating characteristics of the rectifier-side system specifically includes:

[0113] The current low-frequency AC current is detected. If the low-frequency AC current is less than or equal to a preset current threshold, the second output voltage reference value of the rectifier-side converter is calculated according to the first control module, and the inverter-side converter is subjected to fault control according to the second output voltage reference value. The first control module is constructed based on the voltage control loop transmission model of the low-frequency AC voltage.

[0114] If the low-frequency AC current is greater than the preset current threshold, the first output current reference value of the rectifier-side converter is calculated according to the second control module, and the inverter-side converter is subjected to fault control according to the first output current reference value; the second control module is constructed based on the system operating characteristics of the rectifier-side converter.

[0115] In this embodiment, after a short-circuit fault occurs on a low-frequency line in the flexible low-frequency transmission system, the short-circuit current from the flexible low-frequency converter station during the fault transient period mainly consists of two parts: the first part is the current generated by the discharge of the capacitors in the bridge arm submodules of the flexible low-frequency converter station; the second part is the current generated by the energy from the power frequency AC grid passing through the short-circuit point at the transmission point of the flexible low-frequency converter station. After a brief fault dynamic process, the capacitors in the bridge arm submodules of the flexible low-frequency converter station quickly reach an energy balance state. At this time, the operating characteristics of the rectifier-side system of the flexible low-frequency converter station under a low-frequency AC fault are mainly obtained based on the energy transfer process of the power frequency AC grid.

[0116] In this embodiment, since the three-phase bridge arm structure and parameters inside the flexible low-frequency converter station are highly symmetrical, phase A is taken as an example for analysis. Based on the energy transfer model of the power frequency AC grid under low-frequency AC fault, an equivalent circuit model of the flexible low-frequency transmission system is established, specifically as follows:

[0117]

[0118] Among them, L sumC represents the sum of the inductance values ​​in the equivalent circuit of a flexible low-frequency converter station. eq L represents the equivalent capacitance value of the bridge arm in the rectifier-side converter of the flexible low-frequency converter station. bridge The inductance value of the bridge arm in the rectifier-side converter of the flexible low-frequency converter station; u pinv and u ninv These are the upper and lower half-arm voltages of the inverter-side converter in the flexible low-frequency converter station, respectively; n rec n represents the total number of submodules in the single-phase upper and lower half-bridge arms of the rectifier-side converter in a flexible low-frequency converter station. recp This represents the total number of submodules in the single-phase upper half-bridge arm of the rectifier-side converter in a flexible low-frequency converter station; u prec and u nrec These are the upper and lower half-bridge arm voltages of the rectifier-side converter in the flexible low-frequency converter station, respectively; t err This indicates the moment when a low-frequency AC fault occurs.

[0119] In this embodiment, the current system operating status is determined by monitoring the current low-frequency AC current, thereby switching the controller to perform fault control on the inverter-side converter.

[0120] In this embodiment, the calculation of the second output voltage reference value of the rectifier-side converter based on the first control module specifically involves:

[0121] Based on the energy transfer model of the power frequency AC power grid, an equivalent circuit model of the flexible low-frequency power transmission system is constructed.

[0122] A voltage control loop model of the rectifier-side converter is constructed based on the equivalent circuit model of the flexible low-frequency power transmission system, and a first control module is constructed based on the voltage control loop transmission model of the low-frequency AC voltage.

[0123] The second output voltage reference value is calculated based on the first control module. The second output voltage reference value includes a direct-axis voltage reference value and a quadrature-axis voltage reference value.

[0124] In this embodiment, if the low-frequency AC current is less than or equal to a preset current threshold, the system is in normal operation, and a control method based on low-frequency AC voltage is used to control the inverter-side converter for faults.

[0125] In this embodiment, a voltage control loop model of the rectifier-side converter is constructed based on the equivalent circuit model of the flexible low-frequency power transmission system, specifically as follows:

[0126]

[0127] in, and These are the reference values ​​for the d-axis current and q-axis current of the low-frequency AC line in a flexible low-frequency transmission system, respectively. and These are the reference values ​​for the d-axis and q-axis voltages of the low-frequency AC line in a flexible low-frequency transmission system, respectively; u LFACd and u LFACq These are the actual values ​​of the d-axis and q-axis voltages of the low-frequency AC line in a flexible low-frequency transmission system, respectively; G uLFAC (s) is the transfer function of the voltage control loop controller.

[0128] In this embodiment, a first control module is constructed based on the low-frequency AC voltage control loop model, specifically as follows:

[0129]

[0130] in, and These are the reference values ​​for the AC side d-axis voltage and q-axis voltage of the rectifier-side converter in the flexible low-frequency converter station; u d and u q These are the actual values ​​of the AC side d-axis voltage and q-axis voltage of the rectifier-side converter in the flexible low-frequency converter station; G iLFAC (s) is the transfer function of the current control loop controller; ω LFAC For the frequency of flexible low-frequency power transmission systems; i LFACd and i LFACq These represent the actual d-axis and q-axis current values ​​of the low-frequency AC line in a flexible low-frequency transmission system; L LFAC This refers to the inductance of the low-frequency AC line in a flexible low-frequency power transmission system.

[0131] In this embodiment, a second output voltage reference value is calculated based on the first control module. The second output voltage reference value includes the AC side d-axis voltage and q-axis voltage reference values ​​of the rectifier-side converter of the flexible low-frequency converter station.

[0132] In this embodiment, the cutoff frequency of the first control module of the rectifier-side converter of the flexible low-frequency converter station is set to 200Hz, thereby accelerating the response speed of the control loop and reducing the adverse effects of high-frequency noise on the output current waveform quality of the rectifier-side converter of the flexible low-frequency converter station.

[0133] In this embodiment, if the low-frequency AC current is greater than the preset current threshold, a voltage amplitude drop fault occurs in the flexible low-frequency AC line. The output of the low-frequency AC voltage control loop will continue to increase and quickly reach the limit value, making it impossible for the flexible low-frequency converter station to effectively control the low-frequency AC voltage.

[0134] In this embodiment, the calculation of the first output current reference value of the rectifier-side converter based on the second control module specifically involves:

[0135] Based on the energy transfer model of the power frequency AC power grid, an equivalent circuit model of the flexible low-frequency power transmission system is constructed.

[0136] The second control module is constructed based on the equivalent circuit model of the flexible low-frequency power transmission system and the maximum output current of the rectifier-side converter of the flexible low-frequency converter station.

[0137] The second control module calculates a first output current reference value for the low-frequency AC line, which includes a direct-axis current reference value and a quadrature-axis current reference value.

[0138] Fault control is performed on the rectifier-side converter of the flexible low-frequency converter station based on the second output voltage reference value.

[0139] In this embodiment, based on the operating characteristics of the rectifier-side system of the flexible low-frequency converter station under low-frequency AC faults, a second control module is constructed, specifically as follows:

[0140]

[0141] Among them, i LFACmax k represents the maximum output current of the rectifier-side converter in the flexible low-frequency converter station. pmax and k imax For the proportional and integral coefficients of the low-frequency AC fault ride-through control loop controller based on the maximum and minimum current; The voltage threshold for switching the system to a low-frequency AC fault-crossing control loop based on maximum and minimum current; For low-frequency AC system voltage amplitude; i LFACN This refers to the rated output current of the rectifier-side converter in a flexible low-frequency converter station.

[0142] In this embodiment, the cutoff frequency of the second control module of the rectifier-side converter of the flexible low-frequency converter station is set to 1000Hz, thereby accelerating the response speed of the control loop and reducing the adverse effects of high-frequency noise on the output voltage waveform quality of the rectifier-side converter of the flexible low-frequency converter station.

[0143] In this embodiment, when the power frequency AC grid voltage of the flexible low-frequency transmission system changes, the DC bus voltage of the flexible low-frequency converter station changes accordingly. This real-time DC bus voltage is input to the power frequency AC fault ride-through control module. The power frequency AC fault ride-through control module outputs a reference value for the output voltage of the full-bridge submodule group based on the error between the DC bus voltage of the flexible low-frequency converter station and its maximum value. Simultaneously, the expected voltage value of each submodule in the full-bridge submodule group is calculated based on the average voltage of the full-bridge submodules, and then the output voltage compensation of the full-bridge submodule group is obtained according to the output voltage compensation control module. The steady-state reference value of the output voltage of the full-bridge submodule group of the full-bridge distributed pressure relief device is added to the first voltage modulation module to obtain the reference value of the output voltage of the full-bridge submodule group of the full-bridge distributed pressure relief device. The full-bridge submodule group of the full-bridge distributed pressure relief device is modulated according to the reference value and the first voltage modulation module to achieve power frequency AC fault ride-through control.

[0144] In this embodiment, when the low-frequency AC grid voltage of the flexible low-frequency transmission system changes, the low-frequency AC bus voltage of the rectifier-side converter of the flexible low-frequency converter station is input to the first control module. The first control module switches to the second control module, and based on the error between the voltage threshold and the voltage amplitude of the low-frequency AC system, combined with the rated output current of the rectifier-side converter of the flexible low-frequency converter station, outputs the q-axis current reference value of the low-frequency AC line in the flexible low-frequency transmission system. This q-axis current reference value is then calculated by combining it with the maximum output current of the rectifier-side converter of the flexible low-frequency converter station.

[0145] The current control loop of the rectifier-side converter in the flexible low-frequency converter station outputs the AC-side d-axis voltage reference value of the converter based on the error between the d-axis current reference value and the actual d-axis current value of the low-frequency AC line in the flexible low-frequency transmission system, as well as the actual q-axis current value of the low-frequency AC line in the flexible low-frequency transmission system. The current control loop of the rectifier-side converter in the flexible low-frequency converter station also outputs the AC-side q-axis voltage reference value of the converter based on the error between the q-axis current reference value and the actual q-axis current value of the low-frequency AC line in the flexible low-frequency transmission system, as well as the actual d-axis current value of the low-frequency AC line in the flexible low-frequency transmission system.

[0146] In this embodiment, the AC-side d-axis voltage reference values ​​and AC-side q-axis voltage reference values ​​of the rectifier-side converter of the flexible low-frequency converter station are obtained by performing PARK inverse transform and CLARKE inverse transform to obtain the AC-side A-phase voltage reference values, AC-side B-phase voltage reference values, and AC-side C-phase voltage reference values ​​of the rectifier-side converter of the flexible low-frequency converter station. The rectifier-side converter of the flexible low-frequency converter station is modulated based on these AC-side voltage reference values ​​to achieve low-frequency AC fault ride-through control based on maximum and minimum currents.

[0147] In this embodiment, the power frequency AC fault ride-through control module and the low frequency AC fault ride-through control module of the flexible low frequency power transmission system work together to form the fault ride-through control method of the flexible low frequency converter station.

[0148] In this embodiment, the fault ride-through control circuit of the power transmission system further includes a parameter optimization module, which is connected to the power frequency AC fault ride-through control module and the low frequency AC fault ride-through control module respectively.

[0149] The parameter optimization module is used to extract feature vectors of all control modules in the power frequency AC fault ride-through control module and the low frequency AC fault ride-through control module, and to optimize and update the proportional coefficient and integral coefficient of each control module based on the feature vectors.

[0150] In this embodiment, based on the power frequency AC fault ride-through control module and the low frequency AC fault ride-through control module of the flexible low-frequency transmission system, the proportional coefficient k of the output voltage steady-state control module is set. pFB and integral coefficient k iFB The proportional coefficient k of the output voltage compensation control module pFBΔ and integral coefficient k iFBΔ Low-frequency AC fault ride-through control module proportional coefficient k pmax and integral coefficient k imax .

[0151] Based on the structure of the control module, the transfer function form of the controller is extracted, and the proportional coefficient k of each controller is... p With integral coefficient k i Considering two classes of feature samples as features in the feature space, their mean vector in the feature space can be represented as:

[0152]

[0153] Where f(k) is the mapping vector of the high-dimensional feature space; n l The number of feature samples.

[0154] In this embodiment, the square of the distance between the two types of feature samples is obtained based on the mean vector in the feature space:

[0155]

[0156] Wherein, C(k) i ,k j ) is the polynomial kernel function of the feature space, where i and j are the indices of the feature samples, and different variables are used to distinguish them.

[0157] In this embodiment, based on the mean vector in the feature space, the square of the dispersion within the two types of feature samples is obtained as follows:

[0158]

[0159] In this embodiment, the proportional coefficient k of the controller is established based on the square of the distance between the two types of feature samples and the square of the dispersion within the two types of feature samples. p With integral coefficient k i The fitness function, where w is a pre-defined parameter, is:

[0160]

[0161] In this embodiment, based on the proportional coefficient k of the controller p With integral coefficient k i The fitness function w takes values ​​in the range [0.2, 2.0], and the proportional coefficient k of the controller is randomly generated. p With integral coefficient k i In the initial population, calculate the fitness value f of each individual. s and the overall fitness value f of the population g And the proportional coefficient k of the controller is calculated. p With integral coefficient k i Position update and computation speed update, finally determining the number of iterations t num Has the termination condition T been reached? num If the termination condition is reached, the proportional coefficient k of the current controller will be output. p With integral coefficient k i If the optimal control parameters are not used, then the calculation and iteration need to be repeated.

[0162] Please refer to Figure 5 , Figure 5 A waveform diagram of a fault ride-through control method for a flexible low-frequency power transmission system provided in an embodiment of the present invention.

[0163] In this embodiment, the response waveform of the flexible low-frequency transmission system is shown when the three-phase symmetrical voltage of the power frequency AC system drops to 0.5 pu. When a voltage amplitude drop fault occurs in the power frequency AC grid, the power transmission of the flexible low-frequency transmission system is obstructed, causing the DC voltage of the flexible low-frequency converter station to rise. Under the action of the power frequency AC fault ride-through control module, the DC voltage of the flexible low-frequency converter station stabilizes at around 1.05 pu during the fault period, and the flexible low-frequency transmission system can quickly return to normal operation after the fault is restored.

[0164] Please refer to Figure 6 , Figure 6 Another waveform diagram of a fault ride-through control method for a flexible low-frequency power transmission system provided in an embodiment of the present invention.

[0165] In this embodiment, the response waveform of the flexible low-frequency transmission system is shown when the three-phase symmetrical voltage of the low-frequency AC system drops to 0.5 pu. When a voltage amplitude drop fault occurs in the low-frequency AC grid, the current in the low-frequency AC system will rise. Under the action of the low-frequency AC fault ride-through control module, the current in the low-frequency AC system is limited, reducing the risk of equipment damage due to overcurrent. At the same time, the flexible low-frequency transmission system can quickly return to normal operation after the fault is recovered.

[0166] In this embodiment, the power frequency AC fault ride-through control module and the low-frequency AC fault ride-through control module work together to form the fault ride-through control of the flexible low-frequency converter station. The power frequency AC fault ride-through control module suppresses overvoltage phenomena caused by power transmission obstruction on the DC bus voltage of the flexible low-frequency converter station when a voltage dip fault occurs in the power frequency grid, ensuring the safe and reliable operation of the flexible low-frequency converter station and improving the stability of the flexible low-frequency transmission system. The low-frequency AC fault ride-through control module modulates the rectifier-side converter of the flexible low-frequency converter station based on the AC side voltage reference value when a voltage amplitude dip fault occurs on the flexible low-frequency AC line, achieving low-frequency AC fault ride-through control based on the maximum / minimum current.

[0167] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the scope of protection of the present invention. In particular, it should be noted that any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention for those skilled in the art.

Claims

1. A fault ride-through control method for a flexible low-frequency transmission system, characterized in that, include: Detecting fault types in the power transmission system, including power frequency AC faults and low frequency AC faults; If the fault type is a power frequency AC fault, the first output voltage reference value of the inverter-side converter is calculated based on the DC bus voltage, and the inverter-side converter of the flexible low-frequency converter station is subjected to fault control based on the first output voltage reference value. If the fault type is a low-frequency AC fault, then fault control is performed on the rectifier-side converter of the flexible low-frequency converter station according to the operating characteristics of the rectifier-side system. Specifically, the current low-frequency AC current is detected. If the low-frequency AC current is less than or equal to a preset current threshold, then a second output voltage reference value of the rectifier-side converter is calculated according to the first control module, and fault control is performed on the rectifier-side converter according to the second output voltage reference value. The first control module is constructed based on the voltage control loop transmission model of the low-frequency AC voltage. If the low-frequency AC current is greater than the preset current threshold, then a first output current reference value of the rectifier-side converter is calculated according to the second control module, and fault control is performed on the rectifier-side converter according to the first output current reference value. The second control module is constructed based on the system operating characteristics of the rectifier-side converter. The first control module is specifically: in, and These are the reference values ​​for the AC side d-axis voltage and q-axis voltage of the rectifier-side converter in the flexible low-frequency converter station, respectively. and These are the actual values ​​of the AC side d-axis voltage and q-axis voltage of the rectifier-side converter in the flexible low-frequency converter station; G iLFAC (s) is the transfer function of the current control loop controller; ω LFAC For flexible low-frequency power transmission systems; and These are the actual values ​​of the d-axis current and q-axis current of the low-frequency AC line in the flexible low-frequency transmission system, respectively. and These are the d-axis and q-axis current reference values ​​for low-frequency AC lines in a flexible low-frequency transmission system, respectively; L LFAC Inductance for low-frequency AC lines in a flexible low-frequency transmission system; The second control module is specifically: Among them, i LFACmax k represents the maximum output current of the rectifier-side converter in the flexible low-frequency converter station. pmax and k imax For the proportional and integral coefficients of the low-frequency AC fault ride-through control loop controller based on the maximum and minimum current; The voltage threshold for switching the system to a low-frequency AC fault-crossing control loop based on maximum and minimum current; For low-frequency AC system voltage amplitude; i LFACN This refers to the rated output current of the rectifier-side converter in a flexible low-frequency converter station.

2. The fault ride-through control method for a flexible low-frequency transmission system as described in claim 1, characterized in that, The process of calculating the first output voltage reference value of the inverter-side converter based on the DC bus voltage, and performing fault control on the inverter-side converter of the flexible low-frequency converter station based on the first output voltage reference value, specifically includes: Calculate the steady-state reference value of the first output voltage based on the error between the DC bus voltage and the maximum DC bus voltage. Calculate the first voltage compensation value, and calculate the first output voltage reference value of the inverter-side converter based on the first voltage compensation value and the first output voltage steady-state reference value; Fault control is performed on the inverter-side converter of the flexible low-frequency converter station based on the first output voltage reference value. First output voltage steady-state reference value Specifically: Where, k pFB and k iFB These are the proportional and integral coefficients of the power frequency AC fault ride-through control module; U dcmax U represents the maximum DC bus voltage of the flexible low-frequency converter station. dc This refers to the DC bus voltage of the flexible low-frequency converter station. First voltage compensation value Specifically: Where, k pFBΔ and k iFBΔ These are the proportional and integral coefficients of the power frequency AC fault ride-through control module, respectively. U is the average voltage of the full-bridge submodule. FBsmN This represents the expected voltage value of a single full-bridge submodule within the full-bridge submodule group.

3. The fault ride-through control method for a flexible low-frequency transmission system as described in claim 2, characterized in that, The calculation of the second output voltage reference value of the rectifier-side converter based on the first control module is specifically as follows: Based on the energy transfer model of the power frequency AC power grid, an equivalent circuit model of the flexible low-frequency power transmission system is constructed. Based on the equivalent circuit model of the flexible low-frequency power transmission system, a voltage control loop transmission model for the rectifier-side converter is constructed. The first control module is constructed based on the voltage control loop transmission model of the low-frequency AC voltage; The second output voltage reference value is calculated based on the first control module. The second output voltage reference value includes the d-axis voltage reference value and the q-axis voltage reference value.

4. The fault ride-through control method for a flexible low-frequency transmission system as described in claim 1, characterized in that, The calculation of the first output current reference value of the rectifier-side converter based on the second control module is specifically as follows: Based on the energy transfer model of the power frequency AC power grid, an equivalent circuit model of the flexible low-frequency power transmission system is constructed. The second control module is constructed based on the equivalent circuit model of the flexible low-frequency power transmission system and the maximum output current of the rectifier-side converter of the flexible low-frequency converter station. The first output current reference value of the low-frequency AC line is calculated according to the second control module. The first output current reference value includes the d-axis current reference value and the q-axis current reference value. Fault control is performed on the rectifier-side converter of the flexible low-frequency converter station based on the second output voltage reference value.

5. A fault ride-through control circuit for a flexible low-frequency power transmission system, characterized in that, The fault ride-through control method for a power transmission system as described in any one of claims 1 to 4 includes: a power frequency AC fault ride-through control module, a low frequency AC fault ride-through control module, a flexible low frequency converter station, a low frequency AC power grid, and a power frequency AC power grid. The flexible low-frequency converter station includes a rectifier-side converter and an inverter-side converter; the rectifier-side converter is connected to the low-frequency AC power grid; the inverter-side converter is connected to the power frequency AC power grid. The input terminal of the power frequency AC fault ride-through control module is connected to the power frequency AC power grid, and the output terminal of the power frequency AC fault ride-through control module is connected to the inverter-side converter. The input terminal of the low-frequency AC fault ride-through control module is connected to the low-frequency AC power grid, and the output terminal of the low-frequency AC fault ride-through control module is connected to the rectifier-side converter.

6. The fault ride-through control circuit for a flexible low-frequency transmission system as described in claim 5, characterized in that, The power frequency AC fault ride-through control module includes: an output voltage steady-state control module, an output voltage compensation control module, and a first voltage modulation module; The output terminal of the first voltage modulation module is connected to the inverter-side converter, and the input terminal of the first voltage modulation module is connected to the output voltage steady-state control module and the output voltage compensation control module. The first voltage modulation module is used to perform fault control on the inverter-side converter. The output voltage steady-state control module includes a full-bridge submodule group, a bleed resistor, and a smoothing capacitor. The full-bridge submodule group includes several full-bridge submodules connected in series. The full-bridge submodule group and the bleed resistor are connected in series to form an energy discharge path. The energy discharge path and the smoothing capacitor are connected in parallel.

7. The fault ride-through control circuit for a flexible low-frequency transmission system as described in claim 6, characterized in that, The equivalent circuit model of the output voltage steady-state control module is as follows: Among them, U FB U is the output voltage of the full-bridge submodule group. dc Represents the DC bus voltage of the flexible low-frequency converter station; C f For smoothing capacitor, R f For bleed resistor; The output voltage of the full-bridge submodule group is specifically as follows: (1) Where t∈[0,T] Cf ], T Cf U represents the charge / discharge cycle of the full-bridge submodule capacitor; FBmax U represents the maximum output voltage of the full-bridge submodule group. FBmin This is the minimum output voltage of the full-bridge submodule group.

8. The fault ride-through control circuit for a flexible low-frequency transmission system as described in claim 5, characterized in that, The low-frequency AC fault ride-through control module includes a first control module, a second control module, and a second voltage modulation module, wherein the first control module and the second control module are respectively connected to the second voltage modulation module.

9. A fault ride-through control circuit for a flexible low-frequency transmission system as described in any one of claims 5 to 8, characterized in that, The fault ride-through control circuit of the power transmission system further includes a parameter optimization module, which is connected to the power frequency AC fault ride-through control module and the low frequency AC fault ride-through control module respectively. The parameter optimization module is used to extract feature vectors of all control modules in the power frequency AC fault ride-through control module and the low frequency AC fault ride-through control module, and to optimize and update the proportional coefficient and integral coefficient of each control module based on the feature vectors.

Citation Information

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