Stability enhancing method and system applied to back-to-back high-voltage direct current system

Abstract

The invention provides a stability enhancing method and system applied to a back-to-back high-voltage direct-current system, relates to the technical field of power systems, and can effectively enhance the stability of the back-to-back high-voltage direct-current system. The method comprises the following steps: constructing a small signal model of a back-to-back high-voltage direct-current system, wherein the back-to-back high-voltage direct-current system comprises a first voltage source converter and a second voltage source converter; determining a first key state variable dominating high-frequency oscillation in the small-signal model and a second key state variable dominating low-frequency oscillation in the small-signal model through a participation factor analysis mode; determining a high-frequency compensator according to the first key state variable, wherein the high-frequency compensator is used for suppressing high-frequency oscillation; determining a low-frequency compensator according to the second key state variable, wherein the low-frequency compensator is used for suppressing low-frequency oscillation; and integrating the high-frequency compensator and the low-frequency compensator into a control system of the first voltage source converter, and integrating the high-frequency compensator and the low-frequency compensator into a control system of the second voltage source converter.

Description

Technical Field

[0001] This application relates to the technical field of power systems, and particularly to a method and system for enhancing the stability of a back-to-back high-voltage direct current (HVDC) system. Background Art

[0002] With the expansion of the scale of power systems and the increasing demand for new energy grid connection, high-voltage direct current (HVDC) technology has become increasingly important in grid interconnection due to its characteristics of high-efficiency power transmission and flexible control. Among them, voltage source converter (VSC) technology has become the core component of HVDC systems due to its advantages such as independent control of active / reactive power, strong adaptability to weak grids, and small floor area. As a typical application form of VSC-HVDC, the back-to-back (B2B) HVDC system can realize the asynchronous interconnection of different AC systems and has been widely used globally.

[0003] The strength of an AC system is commonly measured by the short circuit ratio (SCR). An SCR lower than 3 indicates a weak system, and lower than 2 indicates an extremely weak grid. Although VSCs can theoretically supply power to an extremely weak grid, however, when a B2B HVDC system connects two extremely weak AC grids with a short circuit ratio (SCR) lower than 2, the stability problem of the system becomes prominent.

[0004] Currently, there is a lack of a solution that can effectively enhance the stability of the system. Summary of the Invention

[0005] This application provides a method and system for enhancing the stability of a back-to-back high-voltage direct current system. Through a comprehensive analysis of the stability of the back-to-back high-voltage direct current system, the dominant factors of the high-frequency instability mechanism and the low-frequency instability mechanism are clarified, and thus a compensation method of adding a multi-objective compensator is proposed, which can effectively enhance the stability of the system.

[0006] In a first aspect, a method for enhancing the stability of a back-to-back high-voltage direct current system is provided, including: Construct a small-signal model of the back-to-back high-voltage direct current system. The back-to-back high-voltage direct current system includes a first voltage source converter and a second voltage source converter. Among them, the first voltage source converter adopts an active power control mode, the second voltage source converter adopts a DC bus voltage control mode. The DC sides of the first voltage source converter and the second voltage source converter are connected through a capacitor, and the AC sides of the first voltage source converter and the second voltage source converter are both connected to the AC grid through an inductor-capacitor filter; By means of participation factor analysis, determine the first key state variable that dominates high-frequency oscillations in the small-signal model and the second key state variable that dominates low-frequency oscillations in the small-signal model; Determine a high-frequency compensator according to the first key state variable, and the high-frequency compensator is used to suppress high-frequency oscillations; Determine a low-frequency compensator according to the second key state variable, and the low-frequency compensator is used to suppress low-frequency oscillations; Integrate the high-frequency compensator and the low-frequency compensator into the control system of the first voltage source converter, and integrate the high-frequency compensator and the low-frequency compensator into the control system of the second voltage source converter. The control systems of the first voltage source converter and the second voltage source converter belong to a back-to-back high-voltage DC system.

[0007] In a feasible design, the control system of the voltage source converter includes an outer-loop control unit, an inner-loop current control unit, and a phase-locked loop unit. The outer-loop control unit is used to control the DC voltage and the voltage at the point of common coupling. The inner-loop current control unit is used to regulate the d-axis current and q-axis current of the voltage source converter. The phase-locked loop unit is used to synchronize the voltage source converter with the AC grid. The voltage source converter is the first voltage source converter or the second voltage source converter, and the AC grid is the AC grid on the side of the first voltage source converter or the AC grid on the side of the second voltage source converter. The small-signal model is: ; Wherein, represents the output value of the small-signal model, represents the characteristic matrix, represents the input matrix, represents the state vector, represents the input vector, The state variables included in contain one or more of the following, represents the d-axis current component on the side of the voltage source converter, represents the q-axis current component on the side of the voltage source converter, represents the d-axis voltage component at the point of common coupling, represents the q-axis voltage component at the point of common coupling, represents the d-axis voltage component on the side of the AC grid, represents the q-axis voltage component on the side of the AC grid, represents the angle of the phase-locked loop phase angle, represents the angular frequency of the phase-locked loop phase angle, represents the DC bus voltage, and the point of common coupling is the connection point between the voltage source converter and the AC grid; Wherein, by means of participation factor analysis, determine the first key state variable that dominates high-frequency oscillations in the small-signal model, including: Derive the partial derivative of the state vector to obtain the element values of the eigenmatrix; Perform eigenvalue decomposition on the eigenmatrix to obtain the eigenvalues corresponding to different frequency modes, and the right and left eigenvectors corresponding to each eigenvalue. The right eigenvector is used to describe the dynamic response direction of the state variables in the frequency mode corresponding to the eigenvalue, and the left eigenvector is used to describe the sensitivity of the eigenvalue to each state variable; For each high-frequency eigenvalue corresponding to the high-frequency mode, determine each first participation factor corresponding to each high-frequency eigenvalue according to the right and left eigenvectors corresponding to each high-frequency eigenvalue. The first participation factor is used to describe the contribution degree of the state variable to the high-frequency eigenvalue; Normalize each first participation factor corresponding to each high-frequency eigenvalue to obtain each normalized first participation factor; Determine the state variables corresponding to the normalized first participation factors greater than the first threshold for each high-frequency eigenvalue as the first key state variables that dominate the high-frequency oscillation.

[0008] In a feasible design, determine the second key state variables that dominate the low-frequency oscillation in the small-signal model through the participation factor analysis method, including: Obtain at least one preset variable, where the preset variable is the transfer function of the DC voltage proportional-integral controller of the outer-loop control unit, the transfer function of the proportional-integral controller of the common connection point, or the transfer function of the proportional-integral controller of the phase-locked loop unit; Add at least one preset variable to the state vector to obtain a new state vector; Derive the partial derivative of the new state vector to obtain the element values of the eigenmatrix; Perform eigenvalue decomposition on the eigenmatrix to obtain the eigenvalues corresponding to different frequency modes, and the right and left eigenvectors corresponding to each eigenvalue. The right eigenvector is used to describe the dynamic response direction of the state variables or preset variables in the frequency mode corresponding to the eigenvalue, and the left eigenvector is used to describe the sensitivity of the eigenvalue to each state variable or preset variable; For each low-frequency eigenvalue corresponding to the low-frequency mode, determine each second participation factor corresponding to each low-frequency eigenvalue according to the right and left eigenvectors corresponding to each low-frequency eigenvalue. The second participation factor is used to describe the contribution degree of the state variables or preset variables to the low-frequency eigenvalue; Normalize each second participation factor corresponding to each low-frequency eigenvalue to obtain each normalized second participation factor; Determine the variables corresponding to the normalized second participation factors greater than the second threshold for each low-frequency eigenvalue as the second key state variables that dominate the low-frequency oscillation, where the variable is a state variable or a preset variable.

[0009] In a feasible design, the first key state variables include the d-axis voltage component of the common connection point and the q-axis voltage component of the common connection point. Determining the high-frequency compensator according to the first key state variables includes: The function of determining the high-frequency compensator according to the first key state variables is to extract the high-frequency component of the common connection point voltage through a high-pass filter and inject the high-frequency component into the inner-loop current control unit to achieve high-frequency oscillation suppression.

[0010] In a feasible design, the transfer function of the high-frequency compensator is: ; Wherein, represents the transfer function of the high-frequency compensator, represents the gain of the high-frequency compensator, represents the complex variable parameter value, represents the cut-off frequency of the high-pass filter.

[0011] In a feasible design, the cut-off frequency is set to 1 / 2 of the frequency of the eigenvalue with the highest vibration frequency among the eigenvalues corresponding to the high-frequency mode.

[0012] In a feasible design, the second key state variables include the angle of the phase-locked loop phase angle, the DC bus voltage, and each preset variable. Determining the low-frequency compensator according to the second key state variables includes: The function of determining the low-frequency compensator according to the second key state variables is to process the disturbance angular frequency of the phase-locked loop unit through a low-pass filter and use the processed disturbance angular frequency as a compensation signal to provide active compensation for the outer-loop control unit of the voltage source converter to achieve low-frequency oscillation suppression.

[0013] In a feasible design, the transfer function of the low-frequency compensator is: ; Wherein, represents the transfer function of the low-frequency compensator, represents the gain of the low-frequency compensator, represents the complex variable parameter value, represents the cut-off frequency of the low-pass filter.

[0014] In a feasible design, the method includes: Determining each key short-circuit ratio corresponding to the first voltage source converter through the trajectories of the eigenvalues of the first voltage source converter, where the key short-circuit ratio is the short-circuit ratio corresponding to the eigenvalue located on the imaginary axis; Determining each key short-circuit ratio corresponding to the second voltage source converter through the trajectories of the eigenvalues of the second voltage source converter; By comparing the respective critical short-circuit ratios corresponding to the first voltage source converter and the respective critical short-circuit ratios corresponding to the second voltage source converter under the same frequency mode, the cut-off frequency of the filter corresponding to the first voltage source converter and the cut-off frequency of the filter corresponding to the second voltage source converter are determined respectively.

[0015] In a second aspect, a stability enhancement system applied to a back-to-back high-voltage DC system is provided, including: A first voltage source converter, and the first voltage source converter adopts an active power control mode; A second voltage source converter, and the second voltage source converter adopts a DC bus voltage control mode. The DC sides of the first voltage source converter and the second voltage source converter are connected through a capacitor, and the AC sides of the first voltage source converter and the second voltage source converter are both connected to the AC power grid through an inductor-capacitor filter; The control system of the first voltage source converter, and the control system of the first voltage source converter includes an outer loop control unit, an inner loop current control unit and a phase-locked loop unit. The outer loop control unit is used to control the DC voltage and the point of common coupling voltage, the inner loop current control unit is used to adjust the d-axis current and q-axis current of the voltage source converter, and the phase-locked loop unit is used to achieve synchronization between the voltage source converter and the AC power grid; The control system of the second voltage source converter, and the control system of the second voltage source converter is the same as that of the first voltage source converter; A high-frequency compensator, which is used to suppress high-frequency oscillations and is integrated into the control systems of the first voltage source converter and the second voltage source converter; A low-frequency compensator, which is used to suppress low-frequency oscillations and is integrated into the control systems of the first voltage source converter and the second voltage source converter.

[0016] In the embodiment of the present application, a detailed small-signal model of the back-to-back high-voltage DC system is constructed, and then a comprehensive stability analysis is carried out on the small-signal model through the participation factor analysis method, clarifying the dominant factors of the high-frequency instability mechanism and the dominant factors of the low-frequency instability mechanism, so as to propose a comprehensive and effective compensation method, that is, adding a multi-objective compensator (including a high-frequency compensator and a low-frequency compensator). In practical applications, the high-frequency compensator of the present application can suppress high-frequency oscillations of 165 Hz by injecting a PCC voltage high-pass signal; the low-frequency compensator reduces the overshoot by 82% by injecting a PLL angular frequency low-pass signal.

[0017] In addition, when SCR = 1, it represents an extremely weak power grid. The power transmission capacity of the power grid is limited, and the power loss is large. Since new energy power generation is often located in remote areas, the local power grid may be in an extremely weak state with SCR = 1, which restricts the connection of new energy to the grid. Currently, to maintain the stable operation of the system, a large number of complex compensation devices need to be installed additionally and special control strategies need to be adopted, increasing the equipment investment and maintenance costs. However, the high-frequency compensator and low-frequency compensator proposed in this application have a simple structure and do not require additional strengthening of the power grid, yet they can enable the B2B HVDC system to transmit power efficiently between extremely weak power grids. For example, in remote areas or areas with weak power grid structures, the energy loss during power transmission can be reduced, the utilization efficiency of power resources can be improved, the power transmission cost can be lowered, the power transmission volume can be increased, the regional electricity demand can be met, and economic development can be promoted. Therefore, the solution of this application can also effectively promote the long-distance transmission of new energy and ensure the power supply stability in remote areas. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] In order to more clearly illustrate the technical solutions of this application, the drawings required for use in the embodiments will be briefly introduced below. Obviously, for those of ordinary skill in the art, other drawings can also be obtained based on these drawings without creative efforts.

[0019] Figure 1 is an example of a stability enhancement method applied to a back-to-back high-voltage DC system provided by an exemplary embodiment of this application; Figure 2 is a schematic structural diagram of a back-to-back high-voltage DC system provided by an exemplary embodiment of this application; Figure 3 is another schematic structural diagram of a back-to-back high-voltage DC system provided by an exemplary embodiment of this application; Figure 4 is a schematic structural diagram of a control system of a voltage source converter provided by an exemplary embodiment of this application; Figure 5 is a schematic diagram of an example of different d-q axis coordinate systems provided by an exemplary embodiment of this application; Figure 6 is a schematic diagram of the eigenvalue movement trajectory of a B2B HVDC system under different frequency modes when the rectifier of VSC1 is operating, provided by an exemplary embodiment of this application; Figure 7 is a schematic diagram of the eigenvalue movement trajectory of a B2B HVDC system under different frequency modes when the inverter of VSC1 is operating, provided by an exemplary embodiment of this application; Figure 8 is a schematic diagram of the eigenvalue movement trajectory of a B2B HVDC system under different frequency modes when the rectifier of VSC2 is operating, provided by an exemplary embodiment of this application; Figure 9 It is a schematic diagram of the eigenvalue movement trajectory under different frequency modes of the B2B HVDC system during the operation of the inverter of VSC2 provided by an exemplary embodiment of the present application; Figure 10 It is a schematic diagram of the analysis result of the participation factors of different eigenvalues corresponding to VSC2 provided by an exemplary embodiment of the present application; Figure 11 It is a schematic diagram of the analysis result of the participation factors of different eigenvalues corresponding to VSC1 provided by an exemplary embodiment of the present application; Figure 12 It is a schematic diagram of the control system structure of the voltage source converter with a compensator added provided by an exemplary embodiment of the present application. Specific Embodiments

[0020] Next, the technical solutions in the embodiments of the present application will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present application without creative efforts shall fall within the protection scope of the present application.

[0021] The present application aims to comprehensively analyze the stability of the B2B HVDC system by establishing a detailed system model, clarify the roots of different instability mechanisms, and propose effective compensation methods, and verify their effectiveness through simulation and real-time hardware-in-the-loop testing.

[0022] Figure 1 It is a method for enhancing the stability applied to a back-to-back high-voltage DC system provided by an exemplary embodiment of the present application, as Figure 1 shown, the method includes: S110, constructing a small-signal model of the back-to-back high-voltage DC system.

[0023] The back-to-back high-voltage DC system includes a first voltage source converter and a second voltage source converter. Among them, the first voltage source converter adopts an active power control mode, the second voltage source converter adopts a DC bus voltage control mode, the DC sides of the first voltage source converter and the second voltage source converter are connected through a capacitor, and the AC sides of the first voltage source converter and the second voltage source converter are both connected to the AC power grid through an inductor-capacitor filter.

[0024] Next, the back-to-back high-voltage DC system built in the present application will be described by way of example in combination with Figure 2 , Figure 3 and Figure 4 for illustration.

[0025] As Figure 2As shown, the constructed back-to-back HVDC system includes a first voltage source converter VSC1 and a second voltage source converter VSC2. The DC sides of the two are connected through a capacitor. VSC1 is connected to the first AC grid (i.e., Figure 2 the grid 1 shown), and VSC2 is connected to the second AC grid (i.e., Figure 2 the grid 2 shown). P in Indicating the input power (i.e., the power flowing into the VSC) reflects the situation of power transmission from the AC side to the inside of the VSC, and its value will change according to the operating state and control strategy of the VSC. For example, in the rectification mode, the VSC absorbs power from the AC grid, P in and it is positive; in the inversion mode, the VSC injects power into the AC grid. Its calculation result still reflects the magnitude of the power flowing from the AC side into the VSC, but at this time the power transmission direction is opposite to that in the rectification mode. Unless otherwise specified, VSC is used to represent VSC1 or VSC2, that is, VSC is a collective term for VSC1 and VSC2. P e Indicating the output power (i.e., the power flowing out of the VSC) can reflect the situation of the VSC outputting power to the outside. Its magnitude and direction also depend on the operating mode and working conditions of the VSC, and the change in its value will affect the stability of the DC bus voltage.

[0026] For VSC1 or VSC2, as Figure 3 shown, the DC sides are all connected through a capacitor and the AC sides are all connected to the AC grid through an inductor-capacitor (LC) filter. Among them, the inductance of the LC filter =57.6 , , represents the DC line current, represents the terminal voltage of the VSC (Terminal Voltage), represents the filter resistance, and its value can be 1.09 . represents the current on the VSC side, represents the active power at the point of common coupling (PCC), represents the reactive power at the PCC. represents the AC grid current of the alternating current system (AC System), represents the AC grid voltage, and its value can be 220 , represents the AC grid inductance, Represents the AC grid resistance.

[0027] Based on the above - built system, the dynamic equations of the AC side of each VSC can be expressed in the d - q axis reference frame of the AC grid as the following formulas (1) and (2): , formula (1); Where, represents the d - axis component of the current on the VSC side, represents the d - axis component of the instantaneous value of the VSC terminal voltage, represents the d - axis component of the instantaneous value of the PCC voltage, represents the angular frequency of the AC grid, represents the imaginary unit. represents the d - axis component of the current on the AC grid side, represents the d - axis component of the instantaneous value of the AC grid side voltage.

[0028] , formula (2); Where, represents the q - axis component of the current on the VSC side, represents the q - axis component of the instantaneous value of the VSC terminal voltage, represents the q - axis component of the instantaneous value of the PCC voltage, represents the angular frequency of the AC grid, represents the imaginary unit. represents the q - axis component of the current on the AC grid side, represents the q - axis component of the instantaneous value of the AC grid side voltage.

[0029] The short - circuit ratio SCR used to define the grid strength is defined as shown in the following formula (3): , formula (3); Where, represents the short - circuit power of the PCC, with the unit of MVA (megavolt - ampere). The short - circuit power reflects the magnitude of the short - circuit current that the AC grid can provide during a short - circuit fault. The larger it is, the stronger the ability of the AC grid to provide short - circuit current in the case of a short - circuit, and the relatively stronger the AC grid. Conversely, the weaker the AC grid. represents the rated power of the VSC. represents the instantaneous value of the AC grid side voltage, represents the equivalent impedance of the grid.

[0030] Vector control is the key to regulating the grid-connected VSC. The architecture of the VSC control system can be divided into an external control loop (i.e., the outer-loop control unit), an internal control loop (i.e., the inner-loop current control unit), and a phase-locked loop unit. The outer-loop control unit is used to control the DC voltage and the PCC voltage. The inner-loop current control unit is used to regulate the d-axis current and q-axis current of the voltage source converter. The phase-locked loop unit is used to synchronize the voltage source converter with the AC grid. The voltage source converter is the first voltage source converter (i.e., VSC1) or the second voltage source converter (i.e., VSC2), and the AC grid is the AC grid on the side of the first voltage source converter or the AC grid on the side of the second voltage source converter. To ensure the rapidity of current response, the bandwidth of the inner-loop current control unit needs to be set relatively large, but it must be lower than the switching frequency of the VSC, generally set at about one-tenth of the switching frequency. In addition, to ensure the stability and robustness of the cascaded control, the bandwidth of the outer-loop control unit is usually designed to be 10% - 20% of the bandwidth of the inner-loop current control unit.

[0031] As Figure 4 shown, the DC voltage control mechanism of the outer-loop control unit generates the d-axis component of the reference current of the VSC, denoted as . This is achieved by comparing the reference value of the required DC bus voltage or the active power setpoint with their respective actual values. Then, the generated error is passed to a proportional-integral (PI) controller.

[0032] Exemplarily, the transient response of the DC bus voltage is enhanced by adding a feedforward component that can predict and compensate for the dynamic changes in the system, thereby accelerating the adjustment speed of the DC bus voltage and maintaining the stability of the DC bus voltage.

[0033] For the d-axis component of the reference current of the VSC for DC bus voltage control can be mathematically described by the following formula (4): , formula (4); where, represents the actual value of the DC link voltage, and the value can be 400 , represents a complex variable, represents the d-axis component of the steady-state value of the PCC voltage, represents the transfer function of the DC voltage PI controller, and the value can be (2720 + 63360) / .

[0034] For the d-axis component of the reference current of the VSC for active power control It can be mathematically described by the following formula (5): , formula (5); Wherein, represents the actual value of the active power set point, represents the transfer function of the active power PI controller.

[0035] The PCC voltage control mechanism uses a PI compensator to solve the difference between the desired voltage and the actual voltage at the PCC. Therefore, the q-axis component of the reference current of the VSC is as shown in the following formula (6): , formula (6); Wherein, represents the reference value of the steady-state value of the PCC voltage, represents the actual measured value of the steady-state value of the PCC voltage, represents the transfer function of the PCC voltage PI controller, and the value can be (631849.32 ) / .

[0036] As Figure 4 shown, the inner-loop current control unit uses a PI compensator to regulate the d-q axis currents (i.e., the d-axis current and the q-axis current) of the VSC. In order to ensure the independent control of the active current and the reactive current, decoupling terms ( and ) are adopted. In addition, PCC voltage feedforward is adopted to mitigate potential voltage disturbances and ensure robust current control. Based on this, the d-axis component and the q-axis component of the actual measured value of the steady-state value of the VSC terminal voltage are as shown in the following formula (7): , formula (7); Wherein, represents the d-axis component of the actual measured value of the steady-state value of the VSC terminal voltage, represents the d-axis component of the actual measured value of the current of the VSC, represents the transfer function of the PI compensator of the inner-loop current control unit, and the value can be (28.8 +545) / , represents the d-axis component of the actual measured value of the steady-state value of the PCC voltage, represents the q-axis component of the actual measured value of the current of the VSC. represents the q-axis component of the actual measured value of the steady-state value of the VSC terminal voltage, represents the q-axis component of the actual measured value of the steady-state value of the PCC voltage.

[0037] The Phase Locked Loop (PLL) control unit is responsible for synchronizing the VSC with the AC grid by estimating the phase angle of the PCC voltage. Under weak grid conditions, the dynamic characteristics of the PLL will significantly affect the performance and stability of the VSC. Therefore, for the stability analysis of the VSC connected to a weak grid, it is crucial to consider the PLL factor. The PLL control unit uses a PI controller to regulate the q-axis component of the PCC voltage to zero and generate the angular frequency. Then, the angular frequency is integrated to generate the synchronization angle, as shown in the following formula (8).

[0038] , formula (8); where represents the synchronization angle of the PCC voltage, that is, the angle of the PLL phase angle, represents the transfer function of the PI controller of the PLL control unit, and the value can be (0.00093 + 0.02457) / , represents the rated angular frequency, represents the d-axis component of the actual measured value of the instantaneous PCC voltage, represents integration.

[0039] The B2B HVDC system involves two independent d-q coordinate systems: the d-q coordinate system of the grid and the d-q coordinate system of the VSC. When the system is in a steady state, these two coordinate systems are synchronized; however, when the system is subjected to transient disturbances, a phase deviation will occur between the two coordinate systems, as shown in Figure 5 . This phase deviation can be attributed to the response time delay of the PLL. Figure 5 in represents the q-axis of the d-q coordinate system of the VSC, represents the d-axis of the d-q coordinate system of the VSC. represents the q-axis of the d-q coordinate system of the grid, represents the d-axis of the d-q coordinate system of the grid. In order to achieve a comprehensive spatial description of the system state, all variables in the grid or VSC coordinate system must be uniformly represented. As shown in Figure 5 , the relationship between the d-q coordinate systems can be represented by the following formula (9): , formula (9); where represents the variable in the converter d-q reference coordinate system, is the variable in the grid d-q reference coordinate system; and are complex factors used to achieve the reference coordinate system transformation, i.e. , represents the synchronous angle of the grid voltage, which is obtained by integrating the angular frequency of the grid voltage.

[0040] Based on the above system, in a feasible design, the small-signal model constructed by this application according to formulas (1) to (7) is shown in the following formula (10). This small-signal model describes the dynamic behavior of the system under different operating states, taking into account not only the fluctuations of the grid voltage but also the influence of the converter control strategy, thus being able to comprehensively reflect the stability characteristics of the back-to-back HVDC system.

[0041] , formula (10); where, represents the output value of the small-signal model, represents the characteristic matrix, represents the input matrix, represents the state vector, represents the input vector, The state variables included in include one or more of represents the d-axis current component on the voltage source converter side, represents the q-axis current component on the voltage source converter side, represents the d-axis voltage component at the point of common coupling, represents the q-axis voltage component at the point of common coupling, represents the d-axis voltage component on the AC grid side, represents the q-axis voltage component on the AC grid side, represents the angle of the phase-locked loop phase angle, represents the angular frequency of the phase-locked loop phase angle, represents the DC bus voltage, and the point of common coupling is the connection point between the voltage source converter and the AC grid.

[0042] In this application, = , , , represents the state vector of VSC1, including . represents the state vector of VSC2, including and . represents the input vector of VSC1, represents the input vector of VSC2.

[0043] In this application, , , Denote the characteristic matrix corresponding to VSC1, Denote the characteristic matrix corresponding to VSC2, Denote the input matrix corresponding to VSC1, Denote the input matrix corresponding to VSC2.

[0044] This application analyzes the stability boundary of the system under different short - circuit ratios (SCRs) by calculating the eigenvalues of the characteristic matrix to assist in designing a more robust back - to - back HVDC system. Among them, the element values of the characteristic matrix are obtained by taking the partial derivative of the state vector. The eigenvalue , and the stability criterion is that the system is unstable when the real part is greater than 0. The damping ratio , which is a key indicator to measure how fast the system vibration decays. The larger the damping ratio, the faster the system vibration decays and the better the stability; conversely, the smaller the damping ratio, the slower the system vibration decays and the worse the stability. By calculating the trajectory of the eigenvalues, the stability boundary of the system under different short - circuit ratios (SCRs) can be identified, and the critical short - circuit ratio (CSCR) can be determined. In this process, the key indicators are the real part (damping) and the imaginary part (vibration frequency) of the eigenvalues. When the SCR decreases, the stability margin of the system decreases, and the eigenvalues gradually approach the imaginary axis (i.e., ), and finally enter the right - hand half - plane (Right Half - Plane, RHP) resulting in instability. At this time, the critical short - circuit ratio at which the system becomes unstable, that is, the critical short - circuit ratio (Critical Short - Circuit Ratio, CSCR), can be determined. CSCR can be understood as the SCR corresponding to the eigenvalue located at , at which time the damping ratio of the system will be very small, meaning that the system vibration will be difficult to decay and the stability is extremely poor.

[0045] Figure 6 Shows the effect of reducing the SCR of Grid 1 from 10 to 1 on the dominant eigenvalues of the B2B HVDC system when the rectifier of VSC1 is in operation. Figure 7 Shows the effect of reducing the SCR of Grid 1 from 10 to 1 on the dominant eigenvalues of the B2B HVDC system when the inverter of VSC1 is in operation. Generally speaking, as the SCR decreases, the stability margin of the system decreases, gradually leading to system instability. Among them, , are the eigenvalues corresponding to the high - frequency mode (High Frequency Mode, HFM), are the eigenvalues corresponding to the low - frequency mode (Low Frequency Mode, LFM), is the eigenvalue corresponding to the medium - frequency mode. Generally, frequencies greater than 100 Hz are called high - frequency, frequencies less than 20 Hz are called low - frequency, and frequencies between the two are called medium - frequency. It can be seen that as the SCR changes, and reach the instability threshold at SCR values of 2.2 and 1.4 respectively, shows instability at a relatively low SCR of 1.15. As Figure 7 shown, when transitioning to the inverter operation of VSC1, it can be seen that as the SCR changes, neither high - frequency nor low - frequency instability is manifested.

[0046] Figure 8 shows the influence of reducing the SCR of grid 2 from 10 to 1 on the dominant eigenvalues of the B2B HVDC system under the rectifier operation of VSC2. Figure 9 shows the influence of reducing the SCR of grid 2 from 10 to 1 on the dominant eigenvalues of the B2B HVDC system under the inverter operation of VSC2. The observed results are similar to those corresponding to VSC1, especially for the high - frequency and low - frequency modes that cause instability under rectifier operation. The HFM represented by and reaches the instability threshold at SCR values of 2.2 and 1.4 respectively. This is consistent with the observations in grid 1, mainly because the two VSCs are connected to AC systems with the same parameters. Figure 9 The in is the eigenvalue corresponding to the medium - frequency mode and enters the unstable state at an SCR of 1.05. Figure 9 The eigenvalue corresponding to the LFM in enters the unstable state at an SCR of 1.

[0047] is the eigenvalue corresponding to the low - frequency mode and shows instability at an SCR of 1.25. However, the eigenvalue corresponding to the low - frequency mode of VSC1 shows instability at an SCR of 1.15. It can be seen that VSC2 becomes unstable at a slightly higher SCR of 1.25. This difference indicates that the VSC2 with DC - bus - voltage control is more vulnerable to instability than the VSC1 with power control in a weak - grid scenario. Therefore, by considering the stability differences under different control modes (DC - bus - voltage control / active - power control) of the VSCs, the unstable factors in the back - to - back HVDC system can be effectively identified and optimized, and the scheme for enhancing the stability of the back - to - back HVDC system can be effectively guided. Based on this consideration, in a feasible design, the method includes: Determining the key short - circuit ratios corresponding to the first voltage - source converter through the trajectories of the eigenvalues of the first voltage - source converter, where the key short - circuit ratio is the short - circuit ratio corresponding to the eigenvalue located on the imaginary axis; Determine the respective critical short-circuit ratios corresponding to the second voltage source converter through the trajectories of the respective eigenvalues of the second voltage source converter; By comparing the respective critical short-circuit ratios corresponding to the first voltage source converter and the respective critical short-circuit ratios corresponding to the second voltage source converter under the same frequency mode, respectively determine the cut-off frequency of the filter corresponding to the first voltage source converter and the cut-off frequency of the filter corresponding to the second voltage source converter.

[0048] For example, by adding low-pass filters with different cut-off frequencies on the VSC side under different control modes, the stability enhancement effect of the system is further optimized. That is, design the cut-off frequency of the low-pass filter of VSC1 to be a lower value to cope with the possible instability under a lower SCR; while design the cut-off frequency of the low-pass filter of VSC2 to be higher than that of the low-pass filter of VSC1 to fully cope with the instability that only occurs under a higher SCR. In this way, the filter parameters can be accurately designed according to the stability characteristics of VSC1 and VSC2 under different control modes, thereby effectively improving the overall stability of the back-to-back HVDC system. In addition, the method may further include monitoring the operating states of VSC1 and VSC2 and adjusting the parameters of the filter in real time to adapt to the changes in the grid state, so as to ensure that the back-to-back HVDC system always maintains good stability.

[0049] In summary, high-frequency oscillation and low-frequency oscillation are the dominant factors of instability in the B2B HVDC system.

[0050] S120, through the participation factor analysis method, determine the first key state variable that dominates high-frequency oscillation in the small-signal model and the second key state variable that dominates low-frequency oscillation in the small-signal model.

[0051] Based on the above small-signal model, the following is the way to determine the first key state variable that dominates high-frequency oscillation in the small-signal model through the participation factor analysis method: Take the partial derivative of the state vector to obtain the respective element values of the eigenmatrix; Perform eigenvalue decomposition on the eigenmatrix to obtain the eigenvalues corresponding to different frequency modes, and the right eigenvector and left eigenvector corresponding to each eigenvalue. The right eigenvector is used to describe the dynamic response direction of the state variable under the corresponding frequency mode of the eigenvalue, and the left eigenvector is used to describe the sensitivity of the eigenvalue to each state variable; For each high-frequency eigenvalue corresponding to the high-frequency mode, according to the right eigenvector and left eigenvector corresponding to each high-frequency eigenvalue, determine the respective first participation factors corresponding to each high-frequency eigenvalue. The first participation factor is used to describe the contribution degree of the state variable to the high-frequency eigenvalue; Perform normalization processing on the respective first participation factors corresponding to each high-frequency eigenvalue to obtain the respective normalized first participation factors; Determine the state variables corresponding to each normalized first participation factor greater than the first threshold among the high-frequency eigenvalue as the first key state variables that dominate the high-frequency oscillation.

[0052] Among them, the first threshold can be set according to actual requirements.

[0053] It should be understood that high-frequency oscillation refers to the operating state of the system reaching an unstable state in the high-frequency mode, while low-frequency oscillation refers to the operating state of the system reaching an unstable state in the low-frequency mode.

[0054] The above embodiments can be implemented through the following steps. Taking VSC2 as an example, it is described as follows: (1) Eigenvalue decomposition: Perform eigenvalue decomposition on the eigenmatrix to obtain each eigenvalue corresponding to the high-frequency mode and its corresponding right eigenvector , where .

[0055] The right eigenvector is used to describe the dynamic response direction of the state variable in the high-frequency mode , and the left eigenvector is used to describe the sensitivity of the high-frequency mode to each state variable.

[0056] Among them, for each eigenvalue , the right eigenvector can be obtained by solving the linear equation system , where represents the identity matrix. The left eigenvector can be obtained by solving the linear equation system

[0057] (2) Calculate the participation factor The first participation factor represents the contribution degree (or influence degree) of the th state variable to the th eigenvalue, and it is the product of the th component in the right eigenvector and the th component in the left eigenvector , , as shown in the following formula (11): , formula (11); (3) Normalization processing: Normalize each of the first participation factors corresponding to each eigenvalue so that their sum is 1, as shown in the following formula (12): , formula (12); Where, represents the after normalization, represents the th state variable's contribution degree to the th eigenvalue, , represents the number of state variables.

[0058] (4) Determine the first key state variable Determine the state variables corresponding to the normalized first participation factors greater than the first threshold for each high-frequency eigenvalue as the first key state variables dominating the high-frequency oscillation.

[0059] The first threshold is set according to actual needs. For example, the value can be 0.1.

[0060] To clarify the degree of influence of each state variable on the eigenvalue, the normalized first participation factors can also be sorted.

[0061] After sorting and screening the normalized first participation factors for each high-frequency eigenvalue, a bar chart of the corresponding normalized first participation factors as shown in Figure 10 is generated. It can be seen that the first key state variables of VSC2 include the state variables , . It should be noted that the subscript "2" in the participation factor in corresponds to VSC2, and the subscript "1" in the participation factor in Figure 10 corresponds to VSC1. Figure 11 For the steps of participation factor analysis of

[0062] and and , refer to the above example and will not be elaborated here.

[0063] For the determination method of the first key state variable of VSC1, refer to the description of the first key state variable of VSC2 and will not be elaborated here. As shown in Figure 11 the bar chart of the corresponding normalized first participation factors of , , the first key state variables of VSC1 include the state variables .

[0064] It should be noted that the main factors affecting the high-frequency mode of the system can be determined as some of the variables in the first key state variables according to requirements.

[0065] It can be seen that the d-axis voltage component and q-axis voltage component of the PCC under the AC grid state are the main factors of the high-frequency mode, and the VSC controller does not affect these modes.

[0066] In the above embodiment, through eigenvalue decomposition and participation factor analysis, the first key state variables that dominate the high-frequency oscillation are determined. The state variables included in the first key state variables have a significant impact on the system dynamic behavior in the high-frequency mode, providing a clear target for the subsequent design of the high-frequency compensator. The calculation and normalization of the participation factor enable the contribution degree of each state variable to the high-frequency eigenvalue to be quantified, so as to clearly identify which state variables are the dominant factors of the high-frequency oscillation. Further, by screening the normalized first participation factor (greater than the first threshold), it is ensured that the selected first key state variables have a high contribution degree, thereby improving the accuracy and reliability of the stability analysis. This example is applicable to back-to-back HVDC systems (such as VSC1 and VSC2) under different control modes, and can adjust the first threshold according to the specific application scenario, enhancing the flexibility and universality of the method.

[0067] This application takes into account that when the DC bus voltage or the PCC voltage fluctuates, it will affect and through the PI compensator, and the control parameters of the phase-locked loop determine the bandwidth, damping and steady-state accuracy of the control loop. If only focusing on the analysis of physical state variables (such as current, voltage, phase angle) for the stability of the system low-frequency mode is not comprehensive enough. In order to comprehensively grasp the dominant factors affecting the stability of the system low-frequency mode, this application also adds the transfer functions of the DC voltage proportional-integral controller of the outer-loop control unit, the proportional-integral controller of the point of common coupling, and the proportional-integral controller of the phase-locked loop unit as preset variables to the analysis, which can quantify their contributions to the low-frequency oscillation and avoid missing key influencing factors. Based on this, in a feasible design, the second key state variables that dominate the low-frequency oscillation in the small-signal model are determined by the following method through participation factor analysis: Obtain at least one preset variable, where the preset variable is the transfer function of the DC voltage proportional-integral controller of the outer-loop control unit, the transfer function of the proportional-integral controller of the point of common coupling, or the transfer function of the proportional-integral controller of the phase-locked loop unit; Add at least one preset variable to the state vector to obtain a new state vector; Take the partial derivative of the new state vector to obtain the values of the elements of the characteristic matrix; Perform eigenvalue decomposition on the eigenmatrix to obtain the eigenvalues corresponding to different frequency modes, as well as the right and left eigenvectors corresponding to each eigenvalue. The right eigenvector is used to describe the dynamic response direction of the state variables or preset variables in the frequency mode corresponding to the eigenvalue, and the left eigenvector is used to describe the sensitivity of the eigenvalue to each state variable or preset variable; For each low-frequency eigenvalue corresponding to the low-frequency mode, determine each second participation factor corresponding to each low-frequency eigenvalue according to the right and left eigenvectors corresponding to each low-frequency eigenvalue. The second participation factor is used to describe the contribution degree of the state variable or preset variable to the low-frequency eigenvalue; Perform normalization processing on each second participation factor corresponding to each low-frequency eigenvalue to obtain each normalized second participation factor; Determine the variables corresponding to the normalized second participation factors greater than the second threshold for each low-frequency eigenvalue as the second key state variables that dominate the low-frequency oscillation, where the variables are state variables or preset variables.

[0068] Among them, the second threshold can be set according to actual needs.

[0069] For example, the obtained preset variables include the transfer function of the DC voltage proportional-integral controller of the outer loop control unit , the transfer function of the proportional-integral controller at the common connection point and the transfer function of the proportional-integral controller of the phase-locked loop unit . Add at least one preset variable to the state vector to obtain a new state vector including , , , . Based on this, represents the new state vector of VSC1, including , (i.e., the corresponding to VSC1), (i.e., the corresponding to VSC1), (i.e., the corresponding to VSC1). represents the new state vector of VSC2, including , , (i.e., the corresponding to VSC2), (i.e., the corresponding to VSC2), (i.e., the corresponding to VSC2). Then take the partial derivative of to obtain the eigenmatrix and Taking VSC2 as an example, for the feature matrix perform eigenvalue decomposition to obtain the eigenvalues corresponding to the low-frequency modes and their corresponding right eigenvectors and left eigenvectors . Among them, . The calculation methods of the right eigenvector and the left eigenvector can be found in and . In addition, for the subsequent steps of calculating the second participation factor and the normalized second participation factor, refer to the relevant examples of the first participation factor and will not be elaborated here. Finally, determine the state variables corresponding to each normalized second participation factor greater than the second threshold for each low-frequency eigenvalue as the second key state variables of the dominant low-frequency oscillation.

[0070] To clarify the degree of influence of each state variable on the eigenvalue, the normalized second participation factors can also be sorted.

[0071] After sorting and screening the normalized first participation factors for each low-frequency eigenvalue, a bar chart of the corresponding normalized first participation factors as shown in Figure 10 is generated. It can be seen that the second key state variables of VSC2 include , , , , and . The above participation factor analysis reveals that the DC bus voltage, external controller state, and PLL state are the main factors of the low-frequency mode.

[0072] For the determination method of the second key state variables of VSC1, refer to the description of the second key state variables of VSC2 and will not be elaborated here. As shown in Figure 11 for the bar chart of the corresponding normalized first participation factors as shown in , the state variables included in the second key state variables of VSC1 are , , and .

[0073] It should be noted that the main factors affecting the low-frequency mode of the system can be determined as some of the variables in the second key state variables according to requirements.

[0074] It can be seen that the main factor affecting the low-frequency mode of the system is the interaction between the PLL and the outer-loop control unit of the VSC. Due to the adverse interaction between the PLL and the outer-loop control unit of the VSC, which is caused by a relatively large PLL bandwidth, exemplarily, the low-frequency oscillation is mitigated by reducing the PLL bandwidth, and the overall system stability is improved.

[0075] In the above embodiment, at least one preset variable is added to the original state vector to form an extended new state vector. Among them, the at least one preset variable includes the transfer function of the DC voltage proportional-integral controller of the outer-loop control unit, the transfer function of the proportional-integral controller of the point of common coupling, and / or the transfer function of the proportional-integral controller of the phase-locked loop unit. Based on the new state vector, through eigenvalue decomposition and participation factor analysis, it can be further determined which state variables have a greater impact on the low-frequency mode of the system, and accurate second key state variables can be obtained. This method not only considers the original state variables, but also introduces the transfer functions related to the outer-loop control unit and the phase-locked loop unit, thereby more comprehensively analyzing the stability of the system. Through this method, the present application can more accurately identify the key factors affecting the system stability, providing strong support for subsequent stability enhancement measures.

[0076] S130, determine a high-frequency compensator according to the first key state variable.

[0077] Among them, the high-frequency compensator is used to suppress high-frequency oscillation.

[0078] In a feasible design, the first key state variable includes the d-axis voltage component of the point of common coupling and the q-axis voltage component of the point of common coupling. It is implemented in the following way to determine the high-frequency compensator according to the first key state variable: The function of determining the high-frequency compensator according to the first key state variable is to extract the high-frequency component of the point of common coupling voltage through a high-pass filter and inject the high-frequency component into the inner-loop current control unit to achieve high-frequency oscillation suppression.

[0079] As Figure 12 shown, two high-frequency compensators need to be set, and the addition positions are shown in the figure. One high-frequency compensator is used to extract the high-frequency component of the d-axis voltage component of the point of common coupling, and one high-frequency compensator is used to extract the high-frequency component of the q-axis voltage component of the point of common coupling.

[0080] In the above example, the high-frequency compensator uses a high-pass filter to extract the frequency mode of the PCC voltage oscillation and then embeds it into a stable closed-loop system. Therefore, these oscillations can be mitigated.

[0081] The participation factor analysis shows that the d-axis voltage component and q-axis voltage component at the common connection point are the main factors of the high-frequency mode. This means that these variables have a high contribution degree in the high-frequency oscillation of the system. Therefore, the high-frequency compensator designed for these key state variables can extract the high-frequency components from the PCC voltage. Then, by feeding back the high-frequency components of the PCC voltage to the inner-loop current control unit, the reference values of the d-axis current and q-axis current of the VSC can be dynamically adjusted, so as to offset the influence of high-frequency oscillation on the system, forming an active compensation mechanism. In addition, due to the high bandwidth and response speed of the inner-loop current control unit, injecting the high-frequency components of the PCC voltage into the inner-loop current control unit can quickly respond to the changes of the high-frequency components, thus improving the effect of the high-frequency compensator in reducing oscillation.

[0082] In a feasible design, the transfer function of the high-frequency compensator is shown in the following formula (13): , formula (13); where, represents the transfer function of the high-frequency compensator, represents the gain of the high-frequency compensator, represents the complex variable, represents the cut-off frequency of the high-pass filter, which can be set to 500 rad / s.

[0083] In the above example, is used to improve the high-frequency damping, and can be adjusted by to stabilize the system and meet the requirements of the stability margin at the same time. For example, it can be set to 0.15 according to the requirements.

[0084] In a feasible design, setting the cut-off frequency to 1 / 2 of the frequency of the eigenvalue with the highest vibration frequency among the eigenvalues corresponding to the high-frequency mode can avoid the transition band region of the filter and effectively reduce the high-frequency oscillation.

[0085] The above embodiments are all applicable to VSC1 and VSC2.

[0086] S140. Determine the low-frequency compensator according to the second key state variable.

[0087] Among them, the low-frequency compensator is used to suppress the low-frequency oscillation.

[0088] In a feasible design, the second key state variables include the angle of the phase-locked loop phase angle, the DC bus voltage and each preset variable. It is realized by the following method: determine the low-frequency compensator according to the second key state variable: Determine the function of the low-frequency compensator according to the second key state variable. The disturbance angular frequency of the phase-locked loop unit is processed by a low-pass filter, and the processed disturbance angular frequency is used as a compensation signal to provide active compensation for the outer-loop control unit of the voltage-source converter, so as to suppress low-frequency oscillations.

[0089] Among them, the addition position of the low-frequency compensator is as Figure 12 shown.

[0090] Through the above-mentioned participation factor analysis, it can be seen that the interaction between the PLL and the outer-loop controller of the VSC under a weak grid (low SCR) is the main factor leading to low-frequency oscillations. The compensation signal in the above example is equivalent to introducing virtual damping into the system, which can reduce the energy accumulation of low-frequency oscillations, thereby realizing low-frequency oscillation suppression.

[0091] In a feasible design, the transfer function of the low-frequency compensator is shown in the following formula (14): , formula (14); Among them, represents the transfer function of the low-frequency compensator, represents the gain of the low-frequency compensator, represents the complex variable parameter value, represents the cut-off frequency of the low-pass filter. can be set to 1700, can be set to 100 rad / s.

[0092] The input of the low-frequency compensator is the disturbance angular frequency , as shown in the following formula (15): , formula (15); It can be seen that the disturbance angular frequency is the difference between two angular frequencies, including only the change in angular frequency and not the steady-state value.

[0093] In the above example, is a stable gain used to improve the low-frequency oscillation damping. The low-pass filter can ensure that only the target low-frequency oscillation is injected into the loop of the VSC outer control unit, providing active compensation for the loop of the VSC outer control unit. Although reducing the PLL bandwidth can mitigate low-frequency oscillations, it may also slow down the system's response speed to dynamic changes, thereby degrading the system's transient performance. In contrast, the above example can provide additional damping to suppress low-frequency oscillations without significantly affecting the system's dynamic response speed by adding a low-frequency compensator. Therefore, compared with reducing the PLL bandwidth, adding a low-frequency compensator can improve the system's transient response and robustness.

[0094] The above embodiments are all applicable to VSC1 and VSC2.

[0095] S150, integrate the high-frequency compensator and the low-frequency compensator into the control system of the first voltage source converter, and integrate the high-frequency compensator and the low-frequency compensator into the control system of the second voltage source converter.

[0096] Among them, the control systems of the first voltage source converter and the second voltage source converter belong to a back-to-back high-voltage DC system.

[0097] Among them, for the adding positions of the high-frequency compensator and the low-frequency compensator, refer to Figure 12 , the high-frequency compensator is located in the inner-loop current control loop, and the low-frequency compensator is located in the outer-loop control feed-forward channel.

[0098] The embodiment of the present application constructs a detailed small-signal model of a back-to-back high-voltage DC system, and then comprehensively analyzes the stability of the small-signal model through the participation factor analysis method, clarifies the dominant factors of the high-frequency instability mechanism and the low-frequency instability mechanism, and thus proposes a comprehensive and effective compensation method, that is, adding a multi-objective compensator (including a high-frequency compensator and a low-frequency compensator). In practical applications, the high-frequency compensator of the present application can suppress the high-frequency oscillation of 165 Hz by injecting a PCC voltage high-pass signal; the low-frequency compensator reduces the overshoot by 82% by injecting a PLL angular frequency low-pass signal.

[0099] In addition, when SCR = 1, it represents an extremely weak power grid, the power transmission capacity of the power grid is limited, and the power loss is large. Since new energy power generation is often located in remote areas, the local power grid may be in an extremely weak state of SCR = 1, which restricts the grid connection of new energy. At present, to maintain the stable operation of the system, a large number of additional complex compensation devices need to be installed and special control strategies need to be adopted, increasing the equipment investment and maintenance costs. However, the high-frequency compensator and the low-frequency compensator proposed in the present application have a simple structure and do not require additional strengthening of the power grid, but can enable the B2B HVDC system to transmit power efficiently between extremely weak power grids. For example, in remote areas or areas with weak power grid structures, the energy loss during power transmission can be reduced, the utilization efficiency of power resources can be improved, the power transmission cost can be reduced, the power transmission volume can be increased, the regional electricity demand can be met, and economic development can be promoted. Therefore, the solution of the present application can also effectively promote the long-distance transmission of new energy and ensure the power supply stability in remote areas.

[0100] The present application also provides a stability enhancement system applied to a back-to-back high-voltage DC system, including: A first voltage source converter, and the first voltage source converter adopts an active power control mode; A second voltage source converter, and the second voltage source converter adopts a DC bus voltage control mode. The DC sides of the first voltage source converter and the second voltage source converter are connected through a capacitor, and the AC sides of the first voltage source converter and the second voltage source converter are both connected to the AC power grid through an inductor-capacitor filter; The control system of the first voltage source converter, which includes an outer-loop control unit, an inner-loop current control unit, and a phase-locked loop unit. The outer-loop control unit is used to control the DC voltage and the voltage at the point of common coupling. The inner-loop current control unit is used to regulate the d-axis current and q-axis current of the voltage source converter. The phase-locked loop unit is used to achieve the synchronization between the voltage source converter and the AC power grid. The control system of the second voltage source converter, which is the same as the control system of the first voltage source converter. The high-frequency compensator, which is used to suppress high-frequency oscillations and is integrated into the control systems of the first voltage source converter and the second voltage source converter. The low-frequency compensator, which is used to suppress low-frequency oscillations and is integrated into the control systems of the first voltage source converter and the second voltage source converter.

[0101] In a feasible design, the function of the high-frequency compensator is to extract the high-frequency component of the voltage at the point of common coupling through a high-pass filter and inject the high-frequency component into the inner-loop current control unit to achieve high-frequency oscillation suppression.

[0102] In a feasible design, the transfer function of the high-frequency compensator is: ; Wherein, represents the transfer function of the high-frequency compensator, represents the gain of the high-frequency compensator, represents the value of the complex variable parameter, represents the cut-off frequency of the high-pass filter.

[0103] In a feasible design, the cut-off frequency is set to 1 / 2 of the frequency of the eigenvalue with the highest vibration frequency among the eigenvalues corresponding to the high-frequency mode.

[0104] In a feasible design, the function of the low-frequency compensator is to process the disturbance angular frequency of the phase-locked loop unit through a low-pass filter and use the processed disturbance angular frequency as a compensation signal to provide active compensation for the outer-loop control unit of the voltage source converter to achieve low-frequency oscillation suppression.

[0105] In a feasible design, the transfer function of the low-frequency compensator is: ; Wherein, represents the transfer function of the low-frequency compensator, represents the gain of the low-frequency compensator, represents the value of the complex variable parameter, represents the cut-off frequency of the low-pass filter.

[0106] For other embodiments and effects of the above system, refer to the descriptions in the method embodiments for enhancing the stability of a back-to-back HVDC system, which will not be elaborated here.

[0107] The basic principles of the present application have been described in conjunction with specific embodiments. However, it should be noted that the advantages, benefits, effects, etc. mentioned in the present application are only examples and not limitations. It cannot be considered that these advantages, benefits, effects, etc. are essential for each embodiment of the present application. Additionally, the specific details disclosed above are only for illustrative and facilitating understanding purposes, rather than limitations. The above details do not limit the present application to necessarily adopt the above specific details for implementation.

[0108] It should be understood that although the steps in the flowcharts of the accompanying drawings are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless clearly stated in this document, the execution of these steps has no strict order limitation and can be executed in other orders. Moreover, at least some of the steps in the flowcharts of the accompanying drawings may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time but can be executed at different times, and their execution order is not necessarily sequential but can be executed alternately or in turn with at least a part of other steps or sub-steps or stages of other steps.

[0109] The block diagrams of the devices, apparatuses, equipment, and systems involved in the present application are only illustrative examples and do not intend to require or imply that they must be connected, arranged, and configured in the manner shown in the block diagrams. As those skilled in the art will recognize, these devices, apparatuses, equipment, and systems can be connected, arranged, and configured in any manner. Words such as "including", "comprising", "having", etc. are open-ended terms meaning "including but not limited to" and can be used interchangeably with each other. The word "or" and "and" used here refer to the word "and / or" and can be used interchangeably with it, unless the context clearly indicates otherwise. The word "such as" used here refers to the phrase "such as but not limited to" and can be used interchangeably with it.

[0110] It also needs to be pointed out that in the devices, equipment, and methods of the present application, each component or each step can be decomposed and / or recombined. These decompositions and / or recombinations should be regarded as equivalent solutions of the present application.

[0111] The above description of the disclosed aspects is provided to enable any person skilled in the art to make or use the present application. Various modifications to these aspects will be readily apparent to those skilled in the art, and the general principles defined herein may be applied to other aspects without departing from the scope of the present application. Thus, the present application is not intended to be limited to the aspects shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

[0112] The above description has been presented for purposes of illustration and description. Furthermore, this description is not intended to limit the embodiments of the present application to the form disclosed herein. Although several example aspects and embodiments have been discussed above, those skilled in the art will recognize some of their variations, modifications, alterations, additions, and subcombinations.

Claims

1. A stability enhancement method applied to a back-to-back high-voltage DC system, characterized in that, Including: Construct a small-signal model of a back-to-back high-voltage direct current (HVDC) system, where the back-to-back HVDC system includes a first voltage source converter and a second voltage source converter. Among them, the first voltage source converter adopts an active power control mode, the second voltage source converter adopts a DC bus voltage control mode, the DC sides of the first voltage source converter and the second voltage source converter are connected through a capacitor, and the AC sides of the first voltage source converter and the second voltage source converter are both connected to the AC grid through an inductance-capacitance filter; Determine a first key state variable that dominates high-frequency oscillation in the small-signal model and a second key state variable that dominates low-frequency oscillation in the small-signal model through participation factor analysis; Determine a high-frequency compensator according to the first key state variable, and the high-frequency compensator is used to suppress high-frequency oscillation; Determine a low-frequency compensator according to the second key state variable, and the low-frequency compensator is used to suppress low-frequency oscillation; Integrate the high-frequency compensator and the low-frequency compensator into the control system of the first voltage source converter, and integrate the high-frequency compensator and the low-frequency compensator into the control system of the second voltage source converter. The control systems of the first voltage source converter and the second voltage source converter belong to the back-to-back HVDC system.

2. The method according to claim 1, wherein The control system of the voltage source converter includes an outer-loop control unit, an inner-loop current control unit, and a phase-locked loop unit. The outer-loop control unit is used to control the DC voltage and the voltage at the point of common coupling. The inner-loop current control unit is used to regulate the d-axis current and q-axis current of the voltage source converter. The phase-locked loop unit is used to achieve synchronization between the voltage source converter and the AC grid. The voltage source converter is the first voltage source converter or the second voltage source converter, and the AC grid is the AC grid on the side of the first voltage source converter or the AC grid on the side of the second voltage source converter. The small-signal model is: ； Among them, represents the output value of the small-signal model, represents the feature matrix, represents the input matrix, represents the state vector, represents the input vector, The included state variables include one or more of those in represents the d-axis current component on the voltage source converter side, represents the q-axis current component on the voltage source converter side, represents the d-axis voltage component at the point of common coupling, represents the q-axis voltage component at the point of common coupling, represents the d-axis voltage component on the AC grid side, represents the q-axis voltage component on the AC grid side, represents the angle of the phase-locked loop phase angle, represents the angular frequency of the phase-locked loop phase angle, represents the DC bus voltage, and the point of common coupling is the connection point between the voltage source converter and the AC grid; Among them, the process of determining the first key state variable that dominates high-frequency oscillation in the small-signal model through participation factor analysis includes: Take the partial derivative of the state vector to obtain the values of each element of the characteristic matrix; Perform eigenvalue decomposition on the characteristic matrix to obtain eigenvalues corresponding to different frequency modes, and the right eigenvector and left eigenvector corresponding to each eigenvalue. The right eigenvector is used to describe the dynamic response direction of the state variable in the frequency mode corresponding to the eigenvalue, and the left eigenvector is used to describe the sensitivity of the eigenvalue to each state variable; For each high-frequency eigenvalue corresponding to the high-frequency mode, determine each first participation factor corresponding to each high-frequency eigenvalue according to the right eigenvector and left eigenvector corresponding to each high-frequency eigenvalue. The first participation factor is used to describe the contribution degree of the state variable to the high-frequency eigenvalue; Perform normalization processing on each first participation factor corresponding to each high-frequency eigenvalue to obtain each normalized first participation factor; Determine the state variables corresponding to the normalized first participation factors greater than the first threshold for each high-frequency eigenvalue as the first key state variables that dominate high-frequency oscillation.

3. The method according to claim 2, wherein Determine the second key state variable that dominates the low-frequency oscillation in the small-signal model by means of participation factor analysis, including: Obtain at least one preset variable, where the preset variable is the transfer function of the DC voltage proportional-integral controller of the outer-loop control unit, the transfer function of the common connection point proportional-integral controller, or the transfer function of the proportional-integral controller of the phase-locked loop unit; Add at least one preset variable to the state vector to obtain a new state vector; Take the partial derivative of the new state vector to obtain the respective element values of the characteristic matrix; Perform eigenvalue decomposition on the characteristic matrix to obtain the eigenvalues corresponding to different frequency modes, and the right eigenvector and left eigenvector corresponding to each eigenvalue. The right eigenvector is used to describe the dynamic response direction of the state variable or preset variable in the frequency mode corresponding to the eigenvalue, and the left eigenvector is used to describe the sensitivity of the eigenvalue to each state variable or preset variable; For each low-frequency eigenvalue corresponding to the low-frequency mode, determine each second participation factor corresponding to each low-frequency eigenvalue according to the right eigenvector and left eigenvector corresponding to each low-frequency eigenvalue. The second participation factor is used to describe the contribution degree of the state variable or preset variable to the low-frequency eigenvalue; Perform normalization processing on each second participation factor corresponding to each low-frequency eigenvalue to obtain each normalized second participation factor; Determine the variables corresponding to the normalized second participation factors greater than the second threshold corresponding to each low-frequency eigenvalue as the second key state variables that dominate the low-frequency oscillation, where the variables are state variables or preset variables.

4. The method according to claim 2, wherein The first key state variables include the d-axis voltage component of the common connection point and the q-axis voltage component of the common connection point. Determining the high-frequency compensator according to the first key state variables includes: The function of determining the high-frequency compensator according to the first key state variables is to extract the high-frequency component of the common connection point voltage through a high-pass filter and inject the high-frequency component into the inner-loop current control unit to achieve high-frequency oscillation suppression.

5. The method according to claim 4, wherein The transfer function of the high-frequency compensator is: ； Among them, represents the transfer function of the high-frequency compensator, represents the gain of the high-frequency compensator, represents the complex variable parameter value, represents the cut-off frequency of the high-pass filter.

6. The method according to claim 5, wherein The cut-off frequency is set to 1 / 2 of the frequency of the eigenvalue with the highest oscillation frequency among the eigenvalues corresponding to the high-frequency mode.

7. The method according to claim 3, wherein The second key state variables include the phase angle of the phase-locked loop, the DC bus voltage, and each preset variable. Determining the low-frequency compensator according to the second key state variables includes: The function of determining the low-frequency compensator according to the second key state variables is to process the disturbance angular frequency of the phase-locked loop unit through a low-pass filter and use the processed disturbance angular frequency as a compensation signal to provide active compensation for the outer-loop control unit of the voltage source converter to achieve low-frequency oscillation suppression.

8. The method according to claim 7, wherein The transfer function of the low-frequency compensator is: ； Among them, represents the transfer function of the low-frequency compensator, represents the gain of the low-frequency compensator, represents the complex variable parameter value, represents the cut-off frequency of the low-pass filter.

9. The method according to any one of claims 2-8, characterized in that, The method includes: Determine the respective critical short-circuit ratios corresponding to the first voltage source converter through the trajectories of the respective eigenvalues of the first voltage source converter. The critical short-circuit ratio is the short-circuit ratio corresponding to the eigenvalue located on the imaginary axis; Determine the respective critical short-circuit ratios corresponding to the second voltage source converter through the trajectories of the respective eigenvalues of the second voltage source converter; By comparing the key short-circuit ratios corresponding to the first voltage source converter and the key short-circuit ratios corresponding to the second voltage source converter under the same frequency mode, the cut-off frequency of the filter corresponding to the first voltage source converter and the cut-off frequency of the filter corresponding to the second voltage source converter are determined respectively.

10. A stability enhancement system applied to a back-to-back high-voltage DC system, characterized in that, Including: A first voltage source converter, which adopts an active power control mode; A second voltage source converter, which adopts a DC bus voltage control mode. The DC sides of the first voltage source converter and the second voltage source converter are connected through a capacitor, and the AC sides of the first voltage source converter and the second voltage source converter are both connected to the AC power grid through an inductor-capacitor filter; The control system of the first voltage source converter, which includes an outer-loop control unit, an inner-loop current control unit and a phase-locked loop unit. The outer-loop control unit is used to control the DC voltage and the voltage at the point of common coupling. The inner-loop current control unit is used to regulate the d-axis current and q-axis current of the voltage source converter. The phase-locked loop unit is used to achieve the synchronization of the voltage source converter and the AC power grid; The control system of the second voltage source converter, which is the same as the control system of the first voltage source converter; A high-frequency compensator, which is used to suppress high-frequency oscillations and is integrated into the control systems of the first voltage source converter and the second voltage source converter; A low-frequency compensator, which is used to suppress low-frequency oscillations and is integrated into the control systems of the first voltage source converter and the second voltage source converter.

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