A magnitude frequency operating point linear time-invariant modeling method and system for lcc-hvdc

Abstract

The application belongs to the technical field of power system modeling, and more particularly to a magnitude-frequency operating point linear time-invariant modeling method and system for LCC-HVDC. A time-invariant model that can accurately reflect the magnitude-frequency state of each three-phase electrical quantity of the rectifier side converter is constructed through the rectifier side phase-locked loop, the current controller, the commutation overlap angle, the internal current magnitude and the internal current frequency. A time-invariant model that can reflect the magnitude-frequency state of each three-phase electrical quantity of the inverter side converter is constructed through the inverter side phase-locked loop, the voltage controller, the commutation overlap angle, the actual trigger lead angle, the power factor angle, the DC voltage, the internal current magnitude and the internal current frequency. Finally, a magnitude-frequency operating point linear time-invariant model that can accurately describe the dynamic evolution process of each three-phase electrical quantity in the LCC-HVDC and the steady-state operating point is obtained through linearization processing of each magnitude-frequency operating point time-invariant model.

Description

Technical Field

[0001] This application belongs to the field of power system modeling technology, and more specifically, relates to a linear time-invariant modeling method and system for amplitude-frequency operating point of LCC-HVDC. Background Technology

[0002] Currently, LCC-HVDC (Line Commutated Converter Based High Voltage Direct Current) power systems play an irreplaceable role in long-distance, high-capacity power transmission. However, as the proportion of renewable energy power equipment at the transmission end increases, the oscillation risk of renewable energy power plants transmitting through the LCC-HVDC system across multiple time scales also increases. Early modeling methods for LCC-HVDC directly used three-phase electrical quantities for description, supporting only single-time-domain simulation analysis and unable to directly extract the system's amplitude and frequency characteristics from the frequency domain. Therefore, linear time-invariant modeling methods, which can be used to explain the interactive oscillation mechanism between multiple devices in a power system, have begun to be widely used.

[0003] Existing linear time-invariant modeling methods, such as dq synchronous rotating coordinate system modeling, typically assume an infinitely large AC power grid (i.e., constant frequency and voltage). They also assume that the dynamic and steady-state values ​​of the terminal voltage frequency have no impact on the calculation of the commutation overlap angle and DC-side voltage of the LCC-HVDC, and introduce the control state variables of local converter equipment into the global model, establishing a non-electrically connected relationship (deep parametric coupling) between the power grid and the equipment. This leads to significant deviations between the simulation model and actual conditions when describing the dynamic evolution of the amplitude and frequency of three-phase electrical quantities and the steady-state operating point in the power system. Furthermore, the introduced non-electrically connected relationship between the power grid and the equipment increases the difficulty of analyzing the interactive oscillation mechanism between the equipment and the power system, thus reducing the accuracy of the assessment results for the interactive stability between the power grid and multiple devices. Summary of the Invention

[0004] To address the aforementioned deficiencies in existing technologies, this application provides a linear time-invariant modeling method and system for amplitude, frequency, and operating point of LCC-HVDC. This aims to solve the problems of existing linear time-invariant modeling methods failing to accurately model the dynamic evolution of the amplitude and frequency of three-phase electrical quantities and the steady-state operating point in LCC-HVDC systems, and the inability to accurately quantify and analyze the interaction stability between various devices and the power system.

[0005] In a first aspect, this application provides a linear time-invariant modeling method for the amplitude-frequency operating point of LCC-HVDC, including: S1. Based on the rectifier-side phase-locked loop and the time-invariant formula of the rectifier-side current controller, obtain the time-invariant formulas of the rectifier-side commutation overlap angle, the actual firing angle, the power factor angle, the DC voltage, the amplitude of the rectifier-side internal current, and the frequency of the rectifier-side internal current. Based on each rectifier-side time-invariant formula, construct a time-invariant model of the rectifier-side amplitude and frequency operating point. S2. Based on the time-invariant formulas of the inverter-side phase-locked loop and inverter-side voltage controller of the inverter-side converter, obtain the time-invariant formulas of the inverter-side commutation overlap angle, the inverter-side actual trigger lead angle, the inverter-side power factor angle, the inverter-side DC voltage, the inverter-side internal current amplitude and the inverter-side internal current frequency, and construct a time-invariant model of the inverter-side amplitude and frequency operating point based on the time-invariant formulas of each inverter side. S3. Based on the time-invariant formulas of the reactive power compensation capacitor, the first single-tuned filter, the second single-tuned filter, and the high-pass filter of the AC filter network, a time-invariant model of the amplitude and frequency operating point of the AC filter network is constructed. The same AC filter network is provided in both the rectifier-side converter and the inverter-side converter. S4. Linearize the amplitude-frequency operating point time-invariant models of the AC filter network, inverter-side converter, and rectifier-side converter at their DC steady-state operating points to obtain the corresponding linear time-invariant models of amplitude-frequency operating points.

[0006] Further, step S1 includes: S11. Based on the rectifier-side phase-locked loop and the time-invariant formula of the rectifier-side current controller, obtain the time-invariant formula of the actual firing angle of the rectifier side; S12. Based on the parameter coupling relationship between the rectifier-side voltage amplitude, rectifier-side voltage angular frequency, rectifier-side DC current and the time-invariant formula of the actual firing angle of the rectifier-side converter, obtain the time-invariant formula of the commutation overlap angle of the rectifier-side converter. S13. Based on the time-invariant formulas of the commutation overlap angle and the actual trigger angle of the rectifier side, obtain the time-invariant formulas of the rectifier side power factor angle, the rectifier side DC voltage, the amplitude of the rectifier side internal current, and the frequency of the rectifier side internal current.

[0007] Furthermore, the time-invariant formula for the actual firing angle on the rectifier side is obtained, including: Based on the parameter coupling relationship between the rectifier-side phase-locked loop angular frequency (PLL angular frequency) and the rectifier-side current controller time-invariant formula, the rectifier-side firing angle command value and the rectifier-side terminal voltage angular frequency and the actual rectifier-side firing angle value of the rectifier-side converter, the time-invariant formula for the actual firing angle of the rectifier side is obtained.

[0008] Furthermore, the time-invariant formula for the commutation overlap angle on the rectifier side is obtained, including: Based on the time-invariant formula for the actual firing angle of the rectifier side, the actual value of the firing angle of the rectifier side, the equivalent inductance of all first transformers of the rectifier-side converter, the amplitude of the rectifier-side terminal voltage, the angular frequency of the rectifier-side terminal voltage, the parameter coupling relationship between the rectifier-side DC current and the rectifier-side commutation overlap angle, the time-invariant formula for the commutation overlap angle of the rectifier side is obtained.

[0009] Further, step S2 includes: S21. Based on the time-invariant formulas of the inverter-side phase-locked loop and the inverter-side voltage controller, obtain the time-invariant formula for the actual trigger lead angle of the inverter side. S22. Based on the parameter coupling relationship between the inverter-side terminal voltage amplitude, inverter-side terminal voltage angular frequency, inverter-side DC current, the second transformer inductance of the inverter-side converter, and the time-invariant formula of the actual trigger lead angle of the inverter side, obtain the time-invariant formula of the inverter-side commutation overlap angle. S23. Based on the time-invariant formulas for the inverter-side commutation overlap angle and the inverter-side actual trigger lead angle, obtain the time-invariant formulas for the inverter-side power factor angle, inverter-side DC voltage, inverter-side internal current amplitude, and inverter-side internal current frequency.

[0010] Furthermore, the time-invariant formula for the actual trigger lead angle on the inverter side is obtained, including: Based on the parameter coupling relationship between the inverter-side phase-locked loop angular frequency (PLL angular frequency) and the inverter-side voltage controller time-invariant formula, the inverter-side trigger lead angle command value and the inverter-side terminal voltage angular frequency and the actual value of the inverter-side trigger lead angle of the inverter-side converter, the time-invariant formula for the actual trigger lead angle of the inverter-side is obtained.

[0011] Furthermore, the time-invariant formula for the inverter-side commutation overlap angle is obtained, including: Based on the time-invariant formula for the actual trigger lead angle of the inverter side, the inductance of the second transformer of the inverter-side converter, the amplitude of the inverter-side terminal voltage, the angular frequency of the inverter-side terminal voltage, the DC current of the inverter side and the commutation overlap angle of the inverter side, the time-invariant formula for the commutation overlap angle of the inverter side is obtained.

[0012] Furthermore, step S4 includes: S41. At the DC steady-state operating point of each time-invariant formula of the target nonlinear function AC filter network, inverter-side converter, and rectifier-side converter amplitude-frequency operating point time-invariant model, a small-signal disturbance is introduced to obtain the target nonlinear function corresponding to each target nonlinear function time-invariant formula, and the target nonlinear function of each target nonlinear function is expanded in the DC steady-state operating point. S42. Remove the nonlinear higher-order terms from the first-order Taylor expansion results of each objective nonlinear function to obtain the linear time-invariant function corresponding to each objective nonlinear function. Based on the linear time-invariant function of each objective nonlinear function, construct the linear time-invariant model of the amplitude-frequency operating point corresponding to the time-invariant model of the amplitude-frequency operating point of each objective nonlinear function.

[0013] Compared to linear time-invariant modeling methods such as dq synchronous rotating coordinate system modeling, the linear model derived from first-order Taylor expansion retains all dynamic partial derivative information at the steady-state operating point. This allows the model to accurately reflect the dynamic evolution of small-signal disturbances in the system under any steady-state frequency scenario, thereby improving the modeling accuracy of the dynamic evolution of the amplitude and frequency of three-phase electrical quantities and the steady-state operating point in the LCC-HVDC system.

[0014] Secondly, this application also provides an amplitude-frequency operating point linear time-invariant modeling system for LCC-HVDC, for performing any of the methods in this aspect, including: The rectifier-side model construction module is used to obtain the rectifier-side commutation overlap angle, rectifier-side actual trigger angle, rectifier-side power factor angle, rectifier-side DC voltage, rectifier-side internal current amplitude and rectifier-side internal current frequency time-invariant formula based on the rectifier-side phase-locked loop and rectifier-side current controller time-invariant formula of the rectifier-side converter, and to construct the rectifier-side amplitude frequency operating point time-invariant model based on each rectifier-side time-invariant formula; The inverter-side model construction module is used to obtain the inverter-side commutation overlap angle, inverter-side actual trigger lead angle, inverter-side power factor angle, inverter-side DC voltage, inverter-side internal current amplitude and inverter-side internal current frequency time-invariant formula based on the inverter-side phase-locked loop and inverter-side voltage controller time-invariant formula of the inverter-side converter, and to construct the inverter-side amplitude and frequency operating point time-invariant model based on the time-invariant formula of each inverter side. The AC filter network model construction module is used to construct a time-invariant model of the amplitude, frequency and operating point of the AC filter network based on the time-invariant formulas of the reactive power compensation capacitor, the first single-tuned filter, the second single-tuned filter and the high-pass filter of the AC filter network. The same AC filter network is provided in both the rectifier-side converter and the inverter-side converter. The linear time-invariant model construction module is used to linearize the DC steady-state operating point of the time-invariant model of the AC filter network, inverter-side converter, and rectifier-side converter at the operating frequency point, so as to obtain the linear time-invariant model of the operating frequency point corresponding to the time-invariant model of each operating frequency point.

[0015] Thirdly, this application also provides an electronic device, characterized in that it comprises: At least one memory for storing computer programs; At least one processor is configured to execute a program stored in the memory, such that, when the program is executed, the processor performs the method described in the first aspect or any possible implementation thereof.

[0016] In summary, the technical solutions conceived by this invention have the following beneficial effects compared with the prior art: This application constructs a time-invariant model that accurately reflects the amplitude and frequency states of each three-phase electrical quantity in the rectifier-side converter by using the rectifier-side phase-locked loop, current controller, commutation overlap angle, actual trigger angle, power factor angle, DC voltage, and time-invariant formulas for internal current amplitude and frequency. Similarly, a time-invariant model reflecting the amplitude and frequency states of each three-phase electrical quantity in the inverter-side converter is constructed using the inverter-side phase-locked loop, voltage controller, commutation overlap angle, actual trigger lead angle, power factor angle, DC voltage, and time-invariant formulas for internal current amplitude and frequency. Finally, by linearizing the time-invariant models of each amplitude and frequency operating point of the LCC-HVDC, a linear time-invariant model of the amplitude and frequency operating point that accurately describes the dynamic evolution of the amplitude and frequency of each three-phase electrical quantity in the LCC-HVDC and its steady-state operating point is obtained.

[0017] Furthermore, the modeling process of this application does not require the introduction of the control state variables of the local converter equipment connected to the LCC-HVDC system into the global model. That is, the LCC-HVDC modeling process does not establish non-electrical connection relationships between the power grid and each device, which can realize the dynamic decoupling between the LCC-HVDC system, the power grid and each device, so that the constructed linear time-invariant model can be used to accurately analyze the interaction stability between the LCC-HVDC system, the power grid and each device. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in this application or related technologies, the accompanying drawings used in the description of the embodiments or related technologies will be briefly introduced below. Obviously, the accompanying drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is a flowchart illustrating the amplitude-frequency operating point linear time-invariant modeling method for LCC-HVDC provided in this application embodiment.

[0020] Figure 2 This is a schematic diagram of the structure of an LCC-HVDC system provided in an embodiment of this application.

[0021] Figure 3This is another schematic diagram of the LCC-HVDC system provided in the embodiments of this application.

[0022] Figure 4 A comparison of the DC current time-domain waveforms of LCC-HVDC system models constructed using different modeling methods provided in the embodiments of this application.

[0023] Figure 5 A modeling framework diagram for the amplitude-frequency operating point linear time-invariant modeling method provided in the embodiments of this application.

[0024] Figure 6 A modeling framework diagram of the dq synchronous rotating coordinate system modeling method provided in the embodiments of this application.

[0025] Figure 7 A schematic diagram of the structure of the amplitude-frequency operating point linear time-invariant modeling system for LCC-HVDC provided in the embodiments of this application.

[0026] Figure 8 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Detailed Implementation

[0027] The technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings.

[0028] In the following description, the terms "second" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance. The following description provides multiple embodiments of this application, which can be substituted or combined with each other. Therefore, this application can also be considered to include all possible combinations of the same and / or different embodiments described. Thus, if one embodiment includes features A, B, and C, and another embodiment includes features B and D, then this application should also be considered to include embodiments containing one or more other possible combinations of A, B, C, and D, even if such embodiments are not explicitly described in the following text.

[0029] The following description provides examples and does not limit the scope, applicability, or examples set forth in the claims. Changes may be made to the function and arrangement of the described elements without departing from the scope of this application. Various processes or components may be appropriately omitted, substituted, or added to the examples. For example, the described methods may be performed in a different order than described, and various steps may be added, omitted, or combined. Furthermore, features described with respect to some examples may be combined into other examples.

[0030] Figure 1This is a flowchart illustrating the amplitude-frequency operating point linear time-invariant modeling method for LCC-HVDC provided in this application embodiment. The method includes the following steps: S1. Based on the rectifier-side phase-locked loop and the time-invariant formula of the rectifier-side current controller, obtain the time-invariant formulas of the rectifier-side commutation overlap angle, the actual trigger angle, the rectifier-side power factor angle, the rectifier-side DC voltage, the amplitude of the rectifier-side internal current, and the frequency of the rectifier-side internal current. Based on each rectifier-side time-invariant formula, construct a time-invariant model of the rectifier-side amplitude and frequency operating point.

[0031] In this embodiment of the application, the executing entity of the method can be the controller of an LCC-HVDC system. For example... Figure 2 and Figure 3 As shown, the LCC-HVDC system consists of a rectifier-side converter, an AC-side converter, and a DC line located between the two converters. Both the rectifier-side and AC-side networks are external power grid networks that supply power to the LCC-HVDC system. The inputs to the rectifier-side converter are the amplitude and angular frequency of the rectifier-side voltage, while the inputs to the inverter-side converter are the amplitude and angular frequency of the inverter-side voltage. For example... Figure 2 As shown, the rectifier-side converter consists of multiple ACFs (AC filters), multiple first transformers, and multiple series-connected six-pulse converter bridges (thyristor converters between the first transformers and the SR). The inverter-side converter consists of multiple ACFs (AC filters), multiple second transformers, and multiple series-connected six-pulse converter bridges (thyristor converters between the SR and the second transformers). Figure 2 In this context, SR (Steady-state Reference Point) refers to the steady-state operating point of the rectifier-side converter or AC-side inverter. The modeling of the rectifier-side converter, inverter-side converter, and AC filter network in this application primarily revolves around this steady-state point. CC (Current Controller) represents the rectifier-side current controller, PLLr (Phase-Locked Loop of Rectifier) ​​represents the rectifier-side phase-locked loop, DVC (DC Voltage Controller) represents the inverter-side voltage controller, and PLLr (Phase-Locked Loop of Rectifier) ​​represents the inverter-side phase-locked loop. Furthermore, PCC (Point of Common Coupling) represents the common coupling point, used to connect the LCC-HVDC system to the power grid network.

[0032] In one possible implementation, step S1 includes: S11. Based on the rectifier-side phase-locked loop and the time-invariant formula of the rectifier-side current controller, obtain the time-invariant formula of the actual firing angle of the rectifier side; S12. Based on the parameter coupling relationship between the rectifier-side voltage amplitude, rectifier-side voltage angular frequency, rectifier-side DC current and the time-invariant formula of the actual firing angle of the rectifier-side converter, obtain the time-invariant formula of the commutation overlap angle of the rectifier-side converter. S13. Based on the time-invariant formulas of the commutation overlap angle and the actual trigger angle of the rectifier side, obtain the time-invariant formulas of the rectifier side power factor angle, the rectifier side DC voltage, the amplitude of the rectifier side internal current, and the frequency of the rectifier side internal current.

[0033] In this embodiment of the application, obtaining the time-invariant formula for the actual firing angle of the rectifier side includes: obtaining the time-invariant formula for the actual firing angle of the rectifier side based on the parameter coupling relationship between the rectifier side phase-locked loop angular frequency of the rectifier side phase-locked loop time-invariant formula, the rectifier side firing angle command value of the rectifier side current controller time-invariant formula, the rectifier side terminal voltage angular frequency of the rectifier side converter, and the actual value of the rectifier side firing angle.

[0034] The time-invariant formula for the angular frequency of the rectifier-side phase-locked loop is: , , ; in, p=d / dt It is a differential operator; A For amplitude, ω Angular frequency, θ For phase; ω r0 The rated angular frequency on the rectifier side. pllr , u tr These represent the rectifier-side phase-locked loop and the rectifier-side terminal voltage, respectively. , These are the proportional and integral coefficients of the phase-locked loop PI controller, respectively. This refers to the intermediate state variables of the rectifier-side phase-locked loop.

[0035] The time-invariant formula for the rectifier-side current controller is: , ; in, α ord,r For the rectifier side firing angle command value, α real,r The actual value of the firing angle on the rectifier side. , These are the proportional and integral coefficients of the PI controller on the rectifier side, respectively. The rectified DC current after filtering, This is the DC current on the rectifier side; This refers to the time constant of the first-order low-pass filter in the AC filter network of this application. I base This is the current reference value.

[0036] The formula for the time-invariant actual firing angle on the rectifier side is: ; in, The angular frequency of the rectifier side voltage. The angular frequency of the rectifier-side phase-locked loop. α ord,r For the rectifier side firing angle command value, α real,r This is the actual value of the firing angle on the rectifier side.

[0037] The time-invariant formula for obtaining the commutation overlap angle on the rectifier side includes: Based on the time-invariant formula for the actual firing angle of the rectifier side, the actual value of the firing angle of the rectifier side, the equivalent inductance of all first transformers of the rectifier-side converter, the amplitude of the rectifier-side terminal voltage, the angular frequency of the rectifier-side terminal voltage, the parameter coupling relationship between the rectifier-side DC current and the rectifier-side commutation overlap angle, the time-invariant formula for the commutation overlap angle of the rectifier side is obtained.

[0038] The time-invariant formula for the commutation overlap angle on the rectifier side is: ; in, μ r This refers to the commutation overlap angle on the rectifier side. L Tr A is the equivalent inductance of the first transformer; tr This represents the voltage amplitude on the rectifier side. It represents the angular frequency of the voltage on the rectifier side. This is the DC current on the rectifier side. α real,r This is the actual value of the firing angle on the rectifier side.

[0039] The time-invariant formula for the rectifier-side power factor is: ; in, φ r The rectifier-side power factor angle. α real,r This is the actual value of the firing angle on the rectifier side. μ r This is the commutation overlap angle on the rectifier side.

[0040] The formula for the time-invariant DC voltage on the rectifier side is: ; in, This is the DC voltage on the rectifier side. This refers to the number of six-pulse commutator bridges in the rectifier-side converter. This refers to the turns ratio of the first transformer. The transformer inductance of a single first transformer.

[0041] The formula for the time-invariant amplitude of the rectifier-side internal current is: ; Among them, A Ir This represents the amplitude of the internal current on the rectifier side.

[0042] The time-invariant formula for the internal frequency of the rectifier side current is: .

[0043] in, ω Ir This is the frequency of the internal current on the rectifier side.

[0044] S2. Based on the time-invariant formulas of the inverter-side phase-locked loop and inverter-side voltage controller of the inverter-side converter, obtain the time-invariant formulas of the inverter-side commutation overlap angle, the inverter-side actual trigger lead angle, the inverter-side power factor angle, the inverter-side DC voltage, the inverter-side internal current amplitude and the inverter-side internal current frequency, and construct a time-invariant model of the inverter-side amplitude and frequency operating point based on the time-invariant formulas of each inverter side.

[0045] In one possible implementation, step S2 includes: S21. Based on the time-invariant formulas of the inverter-side phase-locked loop and the inverter-side voltage controller, obtain the time-invariant formula for the actual trigger lead angle of the inverter side. S22. Based on the parameter coupling relationship between the inverter-side terminal voltage amplitude, inverter-side terminal voltage angular frequency, inverter-side DC current, the second transformer inductance of the inverter-side converter, and the time-invariant formula of the actual trigger lead angle of the inverter side, obtain the time-invariant formula of the inverter-side commutation overlap angle. S23. Based on the time-invariant formulas for the inverter-side commutation overlap angle and the inverter-side actual trigger lead angle, obtain the time-invariant formulas for the inverter-side power factor angle, inverter-side DC voltage, inverter-side internal current amplitude, and inverter-side internal current frequency.

[0046] In this embodiment of the application, obtaining the time-invariant formula for the actual trigger lead angle on the inverter side includes: Based on the parameter coupling relationship between the inverter-side phase-locked loop angular frequency (PLL angular frequency) and the inverter-side voltage controller time-invariant formula, the inverter-side trigger lead angle command value and the inverter-side terminal voltage angular frequency and the actual value of the inverter-side trigger lead angle of the inverter-side converter, the time-invariant formula for the actual trigger lead angle of the inverter-side is obtained.

[0047] Inverter-side phase-locked loop time-invariant formula: , , ; in, This represents the frequency of the inverter-side phase-locked loop. The rated frequency on the inverter side. and These are the proportional and integral parameters of the inverter-side phase-locked loop PI controller. This represents the voltage amplitude on the inverter side. The angle of the phase-locked loop (PLL) at the inverter side voltage. The inverter-side voltage angular frequency, This is the intermediate state variable of the inverter-side phase-locked loop.

[0048] The time-invariant formula for the inverter-side voltage controller is: , ; in, This is the DC voltage filter value on the inverter side. This is the DC voltage on the inverter side. Let be the natural angular frequency of the second-order filter in the AC filter network located on the inverter side. The damping ratio of the second-order filter. and These are the proportional and integral parameters of the DC voltage PI controller on the inverter side. This is the trigger delay angle command value on the inverter side.

[0049] The formula for the invariant actual trigger lead angle on the inverter side is: , ; in, This is the value of the inverter-side lead angle command. This is the actual value of the inverter-side trigger lead angle. Represents the angular frequency of the inverter-side voltage. This represents the angular frequency of the inverter-side phase-locked loop.

[0050] The time-invariant formula for the inverter-side commutation overlap angle is obtained, including: the actual value of the inverter-side trigger lead angle based on the time-invariant formula for the actual trigger lead angle on the inverter side, the inductance of the second transformer of the inverter-side converter, the amplitude of the inverter-side terminal voltage, the angular frequency of the inverter-side terminal voltage, and the parameter coupling relationship between the inverter-side DC current and the inverter-side commutation overlap angle, and the time-invariant formula for the inverter-side commutation overlap angle is obtained.

[0051] Inverter-side commutation overlap angle time-invariant formula: ; in, This refers to the commutation overlap angle on the inverter side. The inductance of the second transformer on the inverter side. This is the DC current on the inverter side. This represents the voltage amplitude on the inverter side. It represents the angular frequency of the inverter-side voltage.

[0052] Inverter-side power factor time-invariant formula: Let , ; in, The inverter-side power factor angle. For the reason Determined auxiliary angle variables, This is the actual value of the inverter-side trigger lead angle. This is the commutation overlap angle on the inverter side.

[0053] Formula for time-invariant DC voltage on the inverter side: ; in, This is the DC voltage on the inverter side. Bi This refers to the number of six-pulse converter bridges on the inverter side (first rectifier).

[0054] Formula for the time-invariant amplitude of the inverter-side internal current: ; in, This represents the amplitude of the internal current on the inverter side.

[0055] The time-invariant formula for the inverter-side internal current frequency: ; in, The frequency of the inverter-side internal current. It represents the angular frequency of the inverter-side voltage.

[0056] S3. Based on the time-invariant formulas of the reactive power compensation capacitor, the first single-tuned filter, the second single-tuned filter, and the high-pass filter of the AC filter network, construct a time-invariant model of the amplitude and frequency operating point of the AC filter network.

[0057] In the embodiments of this application, the same AC filter network is provided in both the rectifier-side converter and the inverter-side converter. Each AC filter network consists of a reactive power compensation capacitor, a first single-tuned filter, a second single-tuned filter, and a high-pass filter. Therefore, it is necessary to perform amplitude-frequency vector space modeling for each component.

[0058] The time-invariant formula for reactive power compensation capacitors is: , , , , , , , .

[0059] in, This refers to the voltage of the reactive power compensation capacitor. , and These represent the inductor currents of the first and second single-tuned filters and the high-pass filter, respectively. A Indicates amplitude. C Indicates capacitance. Represents angular frequency. Indicates phase, A、 、 and C The subscript meaning is the same as the subscript meaning of other parameters; The time-invariant formula for the first single-tuned filter is: , , , , , , , .

[0060] in, This is the capacitor voltage of the first single-tuned filter. The voltage across the resistor of the first single-tuned filter is ; The time-invariant formula for the second single-tuned filter is: , , , , , , , .

[0061] in, This is the capacitor voltage of the second single-tuned filter. This is the voltage across the resistor of the second single-tuned filter; The time-invariant formula for a high-pass filter is: , , , , , , , , .

[0062] in, This is the voltage across the high-pass filter capacitor. This refers to the current component generated across the high-pass filter resistor by the voltage of the reactive power compensation capacitor. This represents the current component generated across the high-pass filter resistor by the voltage across the high-pass filter capacitor.

[0063] S4. Linearize the amplitude-frequency operating point time-invariant models of the AC filter network, inverter-side converter, and rectifier-side converter at their DC steady-state operating points to obtain the corresponding linear time-invariant models of amplitude-frequency operating points.

[0064] In one possible implementation, step S4 includes: S41. At the DC steady-state operating point of each time-invariant formula of the target nonlinear function AC filter network, inverter-side converter, and rectifier-side converter amplitude-frequency operating point time-invariant model, a small-signal disturbance is introduced to obtain the target nonlinear function corresponding to each target nonlinear function time-invariant formula, and the target nonlinear function of each target nonlinear function is expanded in the DC steady-state operating point. S42. Remove the nonlinear higher-order terms from the first-order Taylor expansion results of each objective nonlinear function to obtain the linear time-invariant function corresponding to each objective nonlinear function. Based on the linear time-invariant function of each objective nonlinear function, construct the linear time-invariant model of the amplitude-frequency operating point corresponding to the time-invariant model of the amplitude-frequency operating point of each objective nonlinear function.

[0065] In this embodiment, the method for linearizing the time-invariant model at each amplitude frequency operating point is similar. Therefore, this embodiment only takes the linearization process of the rectifier-side phase-locked loop linear time-invariant formula as an example. The process of obtaining the rectifier-side phase-locked loop linear time-invariant formula is as follows: Near the DC steady-state operating point of the invariant formula of the rectifier-side phase-locked loop, a small-signal disturbance is introduced: , , , ,

[0066] Where the superscript 0 indicates the variable value at the steady-state operating point, This represents the corresponding small-signal perturbation. A For amplitude, ω Angular frequency, θ For phase; ω r0 The rated angular frequency on the rectifier side. pllr , u tr These represent the rectifier-side phase-locked loop and the rectifier-side terminal voltage, respectively. , These are the proportional and integral coefficients of the phase-locked loop PI controller, respectively. This refers to the intermediate state variables of the rectifier-side phase-locked loop.

[0067] Original inverter-side phase-locked loop time-invariant formula: , , ; After introducing small signal perturbation Defined as the first objective nonlinear function: Then there is

[0068] Performing a first-order Taylor expansion of function f1 at the steady-state operating point, we obtain:

[0069] The partial derivatives are: , ,

[0070] Therefore, we get:

[0071] When the system is stable, there are usually ,therefore ,

[0072] Therefore, we get:

[0073] After introducing small signal perturbation , defined as the second objective nonlinear function:

[0074] Then we have:

[0075] A first-order Taylor expansion of f2 at the steady-state operating point:

[0076] in: , .

[0077] Therefore, we get:

[0078] exist At that time,

[0079] For the phase error equation: The equation itself is a linear relationship, and we can directly obtain the result by taking the disturbance amount:

[0080] Therefore, the linear time-invariant function of the phase-locked loop (the small-signal linearization function of the phase-locked loop) based on the first-order Taylor expansion is: , ,

[0081] Similarly, by applying the same first-order Taylor expansion linearization process to each time-invariant function, the corresponding linear time-invariant function can be obtained. Since the linearized version of the time-invariant model of the AC filter network amplitude, frequency, and operating point is quite lengthy, it will not be specifically shown in the embodiments of this application.

[0082] The linear time-invariant formula for the rectifier-side current controller is: , ; The actual firing angle is linearly time-invariant, and the formula is: ; The time-invariant formula for the linear commutation overlap angle is: ; The formula for the time-invariant power factor angle is: ; The time-invariant formula for the linear current and voltage of a DC capacitor is:

[0083] The formula for linear time-invariant internal current amplitude is: ; The formula for the linear time-invariant internal current frequency is: ; The linear time-invariant formula for the inverter-side phase-locked loop is: , , ; Linear time-invariant formula for inverter-side control loop: , , ; The time-invariant formula for the actual lead angle on the inverter side: , ; Inverter-side commutation overlap angle linear time-invariant formula: ; The time-invariant formula for the inverter-side power factor angle is linear: , ; The time-invariant formula for the linear DC voltage on the inverter side: ; The time-invariant formula for the linear amplitude of the inverter-side internal current: ; The time-invariant formula for the linear frequency of the inverter-side internal current is as follows: .

[0084] In the embodiments of this application, such as Figure 4 As shown, this application also constructs the amplitude-frequency operating point linear time-invariant model (AVM_) of the LCC-HVDC system in MATLAB / Simulink. A ), dq coordinate system average value model (AVM_ dq The model is compared with the Detailed Switch Model (DSM). The power per unit value of the grid device is set for each model. At the 3s, a square wave signal with a duration of 0.01s and an amplitude of 0.01pu is generated. The DC current waveform of the LCC-HVDC rectifier side of the three models is observed.

[0085] like Figure 4 As shown, the waveform comparison reveals that the oscillation frequencies of the mathematical model based on the dq coordinate system and the electromagnetic model are inconsistent. However, the amplitude-frequency operating point linear time-invariant model constructed based on the method of this application basically matches the oscillation frequency of the electromagnetic model, which can effectively verify the accuracy of the modeling results of the method of this application.

[0086] like Figure 5 and Figure 6 As shown in the figure, the differences in the modeling framework between the dq synchronous rotating coordinate system modeling method and the modeling method of this application are illustrated. I sg and U sgThis represents the current and terminal voltage introduced into each device by the synchronizing machine. The superscript indicates the different device numbers (e.g., synchronizing machine is labeled 1, device 2 is labeled 2), and the subscript indicates different modeling methods. This represents the angular frequency of the synchronous machine. Compared to linear time-invariant modeling methods such as dq synchronous rotating coordinate system modeling, the linear model derived from the first-order Taylor expansion retains all dynamic partial derivative information at the steady-state operating point while eliminating the need to include the control state variables of the local converter equipment (such as...). Figure 6 middle I sg , U sg and This is incorporated into the global model. This enables the amplitude-frequency operating point linear time-invariant model constructed by the method in this application to accurately reflect the dynamic evolution of small-signal disturbances in the system under any steady-state frequency scenario. This allows for the decoupling of various devices from the AC network (power grid) and its use in analyzing the impact of LCC-HVDC or other grid-connected devices on the stability of the power grid system.

[0087] Figure 7 This is a schematic diagram of the structure of the amplitude-frequency operating point linear time-invariant modeling system for LCC-HVDC provided in the embodiments of this application, as shown below. Figure 7 As shown, the system includes at least: The rectifier-side model construction module is used to obtain the rectifier-side commutation overlap angle, rectifier-side actual trigger angle, rectifier-side power factor angle, rectifier-side DC voltage, rectifier-side internal current amplitude and rectifier-side internal current frequency time-invariant formula based on the rectifier-side phase-locked loop and rectifier-side current controller time-invariant formula of the rectifier-side converter, and to construct the rectifier-side amplitude frequency operating point time-invariant model based on each rectifier-side time-invariant formula; The inverter-side model construction module is used to obtain the inverter-side commutation overlap angle, inverter-side actual trigger lead angle, inverter-side power factor angle, inverter-side DC voltage, inverter-side internal current amplitude and inverter-side internal current frequency time-invariant formula based on the inverter-side phase-locked loop and inverter-side voltage controller time-invariant formula of the inverter-side converter, and to construct the inverter-side amplitude and frequency operating point time-invariant model based on the time-invariant formula of each inverter side. The AC filter network model construction module is used to construct a time-invariant model of the amplitude, frequency and operating point of the AC filter network based on the time-invariant formulas of the reactive power compensation capacitor, the first single-tuned filter, the second single-tuned filter and the high-pass filter of the AC filter network. The same AC filter network is provided in both the rectifier-side converter and the inverter-side converter. The linear time-invariant model construction module is used to linearize the DC steady-state operating point of the time-invariant model of the AC filter network, inverter-side converter, and rectifier-side converter at the operating frequency point, so as to obtain the linear time-invariant model of the operating frequency point corresponding to the time-invariant model of each operating frequency point.

[0088] like Figure 8 As shown, Figure 8 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. The electronic device may include: a processor 801, a communications interface 802, a memory 803, and a communication bus 804. The processor 801, communications interface 802, and memory 803 communicate with each other via the communication bus 804. The processor 801 can call software instructions in the memory 803 to execute the methods described in the above embodiments.

[0089] Furthermore, the logical instructions in the aforementioned memory 803 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this application.

[0090] Based on the methods in the above embodiments, this application provides a computer-readable storage medium storing a computer program that, when run on a processor, causes the processor to execute the methods in the above embodiments.

[0091] Based on the methods in the above embodiments, this application provides a computer program product that, when run on a processor, causes the processor to execute the methods in the above embodiments.

[0092] It is understood that the processor in the embodiments of this application can be a CPU (Central Processing Unit), or other general-purpose processors, DSPs (Digital Signal Processors), ASICs (Application Specific Integrated Circuits), FPGAs (Field Programmable Gate Arrays), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. A general-purpose processor can be a microprocessor or any conventional processor.

[0093] The method steps in this application embodiment can be implemented in hardware or by a processor executing software instructions. The software instructions can consist of corresponding software modules, which can be stored in random access memory (RAM), flash memory, ROM (Read-only Memory), PROM (Programmable ROM), EPROM (Erasable PROM), EEPROM (Electrically Erasable EPROM), registers, hard disks, portable hard disks, CD-ROMs, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor, enabling the processor to read information from and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and the storage medium can reside in an ASIC.

[0094] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as a computer program product. A computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the flow or function according to the embodiments of this application is generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in or transmitted through a computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line DSL) or wireless (e.g., infrared, wireless, microwave, etc.). The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., SSD (Solid State Disk)).

[0095] It is understood that the various numerical designations used in the embodiments of this application are merely for the convenience of description and are not intended to limit the scope of the embodiments of this application.

[0096] Those skilled in the art will readily understand that the above are merely preferred embodiments of this application and are not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A linear time-invariant modeling method for amplitude-frequency operating point of LCC-HVDC, characterized in that, include: S1. Based on the rectifier-side phase-locked loop and the time-invariant formula of the rectifier-side current controller, obtain the time-invariant formulas of the rectifier-side commutation overlap angle, the actual firing angle, the power factor angle, the DC voltage, the amplitude of the rectifier-side internal current, and the frequency of the rectifier-side internal current. Based on each rectifier-side time-invariant formula, construct a time-invariant model of the rectifier-side amplitude and frequency operating point. S2. Based on the time-invariant formulas of the inverter-side phase-locked loop and inverter-side voltage controller of the inverter-side converter, obtain the time-invariant formulas of the inverter-side commutation overlap angle, the inverter-side actual trigger lead angle, the inverter-side power factor angle, the inverter-side DC voltage, the inverter-side internal current amplitude and the inverter-side internal current frequency, and construct a time-invariant model of the inverter-side amplitude and frequency operating point based on the time-invariant formulas of each inverter side. S3. Based on the time-invariant formulas of the reactive power compensation capacitor, the first single-tuned filter, the second single-tuned filter, and the high-pass filter of the AC filter network, a time-invariant model of the amplitude-frequency operating point of the AC filter network is constructed. The same AC filter network is provided in both the rectifier-side converter and the inverter-side converter. S4. Linearize the amplitude-frequency operating point time-invariant models of the AC filter network, inverter-side converter, and rectifier-side converter at their DC steady-state operating points to obtain the amplitude-frequency operating point linear time-invariant models corresponding to each amplitude-frequency operating point time-invariant model.

2. The amplitude-frequency operating point linear time-invariant modeling method according to claim 1, characterized in that, Step S1 includes: S11. Based on the rectifier-side phase-locked loop and the time-invariant formula of the rectifier-side current controller, obtain the time-invariant formula of the actual firing angle of the rectifier side; S12. Based on the parameter coupling relationship between the rectifier-side terminal voltage amplitude, rectifier-side terminal voltage angular frequency, rectifier-side DC current and the time-invariant formula of the actual firing angle of the rectifier-side converter, obtain the time-invariant formula of the rectifier-side commutation overlap angle. S13. Based on the time-invariant formulas for the commutation overlap angle and the actual trigger angle of the rectifier side, obtain the time-invariant formulas for the power factor angle of the rectifier side, the DC voltage of the rectifier side, the amplitude of the internal current of the rectifier side, and the frequency of the internal current of the rectifier side.

3. The amplitude-frequency operating point linear time-invariant modeling method according to claim 2, characterized in that, The formula for obtaining the actual firing angle on the rectifier side is invariant and includes: Based on the parameter coupling relationship between the rectifier-side phase-locked loop angular frequency of the rectifier-side phase-locked loop time-invariant formula, the rectifier-side trigger angle command value of the rectifier-side current controller time-invariant formula, the rectifier-side terminal voltage angular frequency of the rectifier-side converter, and the actual value of the rectifier-side trigger angle, the time-invariant formula for the actual rectifier-side trigger angle is obtained.

4. The amplitude-frequency operating point linear time-invariant modeling method according to claim 2, characterized in that, The time-invariant formula for obtaining the commutation overlap angle on the rectifier side includes: Based on the actual value of the rectifier-side firing angle obtained from the time-invariant formula of the actual firing angle of the rectifier side, the equivalent inductance of all first transformers of the rectifier-side converter, the amplitude of the rectifier-side terminal voltage, the angular frequency of the rectifier-side terminal voltage, and the parameter coupling relationship between the rectifier-side DC current and the rectifier-side commutation overlap angle, the time-invariant formula of the rectifier-side commutation overlap angle is obtained.

5. The amplitude-frequency operating point linear time-invariant modeling method according to claim 1, characterized in that, Step S2 includes: S21. Based on the time-invariant formulas of the inverter-side phase-locked loop and the inverter-side voltage controller, obtain the time-invariant formula for the actual trigger lead angle of the inverter side. S22. Based on the parameter coupling relationship between the inverter-side terminal voltage amplitude, inverter-side terminal voltage angular frequency, inverter-side DC current, the second transformer inductance of the inverter-side converter, and the time-invariant formula of the actual trigger lead angle of the inverter side, obtain the time-invariant formula of the inverter-side commutation overlap angle. S23. Based on the time-invariant formulas for the inverter-side commutation overlap angle and the inverter-side actual trigger lead angle, obtain the time-invariant formulas for the inverter-side power factor angle, inverter-side DC voltage, inverter-side internal current amplitude, and inverter-side internal current frequency.

6. The amplitude-frequency operating point linear time-invariant modeling method according to claim 1, characterized in that, The formula for obtaining the actual trigger lead angle on the inverter side is time invariant and includes: Based on the parameter coupling relationship between the inverter-side phase-locked loop angular frequency of the inverter-side phase-locked loop time-invariant formula, the inverter-side trigger lead angle command value of the inverter-side voltage controller time-invariant formula, the inverter-side terminal voltage angular frequency of the inverter-side converter, and the actual value of the inverter-side trigger lead angle, the time-invariant formula for the actual trigger lead angle of the inverter side is obtained.

7. The amplitude-frequency operating point linear time-invariant modeling method according to claim 1, characterized in that, The time-invariant formula for obtaining the inverter-side commutation overlap angle includes: Based on the actual value of the inverter-side trigger lead angle, the second transformer inductance of the inverter-side converter, the inverter-side terminal voltage amplitude, the inverter-side terminal voltage angular frequency, the inverter-side DC current and the inverter-side commutation overlap angle, the time-invariant formula for the inverter-side commutation overlap angle is obtained.

8. The amplitude-frequency operating point linear time-invariant modeling method according to claim 1, characterized in that, Step S4 includes: S41. At the DC steady-state operating point of each time-invariant formula of the time-invariant model of the amplitude-frequency operating point of the AC filter network, inverter-side converter, and rectifier-side converter, a small-signal disturbance is introduced to obtain the target nonlinear function corresponding to each time-invariant formula, and the target nonlinear function is expanded in first order Taylor at the DC steady-state operating point. S42. Remove the nonlinear higher-order terms from the first-order Taylor expansion results of each of the target nonlinear functions to obtain the linear time-invariant function corresponding to each of the target nonlinear functions, and construct the linear time-invariant model of the amplitude frequency operating point corresponding to each of the amplitude frequency operating point time-invariant models based on each of the linear time-invariant functions.

9. A linear time-invariant modeling system for amplitude-frequency operating point of LCC-HVDC, used to perform the method as described in any one of claims 1-8, characterized in that, include: The rectifier-side model construction module is used to obtain the rectifier-side commutation overlap angle, rectifier-side actual trigger angle, rectifier-side power factor angle, rectifier-side DC voltage, rectifier-side internal current amplitude and rectifier-side internal current frequency time-invariant formula based on the rectifier-side phase-locked loop and rectifier-side current controller time-invariant formula of the rectifier-side converter, and to construct the rectifier-side amplitude frequency operating point time-invariant model based on each rectifier-side time-invariant formula; The inverter-side model construction module is used to obtain the inverter-side commutation overlap angle, inverter-side actual trigger lead angle, inverter-side power factor angle, inverter-side DC voltage, inverter-side internal current amplitude and inverter-side internal current frequency time-invariant formula based on the inverter-side phase-locked loop and inverter-side voltage controller time-invariant formula of the inverter-side converter, and to construct the inverter-side amplitude and frequency operating point time-invariant model based on the time-invariant formula of each inverter side. An AC filter network model construction module is used to construct a time-invariant model of the amplitude, frequency, and operating point of the AC filter network based on the time-invariant formulas of the reactive power compensation capacitor, the first single-tuned filter, the second single-tuned filter, and the high-pass filter of the AC filter network. The same AC filter network is provided in both the rectifier-side converter and the inverter-side converter. The linear time-invariant model construction module is used to linearize the DC steady-state operating point of the amplitude-frequency operating point time-invariant model of the AC filter network, inverter-side converter, and rectifier-side converter to obtain the amplitude-frequency operating point linear time-invariant model corresponding to each amplitude-frequency operating point time-invariant model.

10. An electronic device, characterized in that, include: At least one memory for storing computer programs; At least one processor is configured to execute a program stored in the memory, wherein when the program stored in the memory is executed, the processor is configured to perform the method as described in any one of claims 1-8.

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