A stability enhancement method and system for back-to-back high voltage direct current systems

Abstract

The present application provides a stability enhancement method and system for a back-to-back high-voltage direct current (HVDC) system, which relates to the field of power system technology and can effectively enhance the stability of the back-to-back HVDC system. The method includes: constructing a small-signal model of the back-to-back HVDC system, wherein the back-to-back HVDC system includes a first voltage source converter and a second voltage source converter; determining a first key state variable that dominates high-frequency oscillations in the small-signal model and a second key state variable that dominates low-frequency oscillations in the small-signal model by means of a participation factor analysis method; determining a high-frequency compensator based on the first key state variable, wherein the high-frequency compensator is used to suppress high-frequency oscillations; determining a low-frequency compensator based on the second key state variable, wherein the low-frequency compensator is used to suppress low-frequency oscillations; integrating the high-frequency compensator and the low-frequency compensator into the control system of the first voltage source converter, and integrating the high-frequency compensator and the low-frequency compensator into the control system of the second voltage source converter.

Description

Technical Field

[0001] The present application relates to the technical field of power systems, and in particular to a stability enhancement method and system for a back-to-back high-voltage direct current system. Background Art

[0002] As power systems expand and demand for renewable energy integration grows, High Voltage Direct Current (HVDC) technology is becoming increasingly important in grid interconnection due to its efficient transmission and flexible control features. Voltage Source Converter (VSC) technology, with its advantages such as independent control of active and reactive power, strong adaptability to weak grids, and compact footprint, has become a core component of HVDC systems. Back-to-back (B2B) HVDC systems, a typical application of VSC-HVDC, enable asynchronous interconnection of different AC systems and have been widely adopted worldwide.

[0003] AC system strength is often measured using the Short Circuit Ratio (SCR). An SCR below 3 indicates a weak system, and below 2 indicates an extremely weak grid. While VSCs can theoretically supply power to extremely weak grids, when a B2B HVDC system connects two extremely weak AC grids with an SCR below 2, system stability issues become prominent.

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

[0005] The present application provides a stability enhancement method and system for a back-to-back high-voltage direct current (HVDC) system. By comprehensively analyzing the stability of the back-to-back HVDC system, the dominant factors of the high-frequency instability mechanism and the dominant factors of the low-frequency instability mechanism are identified, thereby proposing a compensation method by adding a multi-objective compensator, which can effectively enhance the stability of the system.

[0006] In a first aspect, a stability enhancement method for a back-to-back high voltage direct current system is provided, comprising:

[0007] Constructing a small signal model of a back-to-back high-voltage direct current (HVDC) system, the back-to-back HVDC system comprising a first voltage source converter and a second voltage source converter, wherein 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 via a capacitor, and the AC sides of the first voltage source converter and the second voltage source converter are both connected to an AC power grid via an inductor-capacitor filter;

[0008] By means of participating factor analysis, the first key state variable that dominates the high-frequency oscillation in the small signal model and the second key state variable that dominates the low-frequency oscillation in the small signal model are determined;

[0009] determining a high-frequency compensator according to the first key state variable, where the high-frequency compensator is used to suppress high-frequency oscillation;

[0010] determining a low-frequency compensator according to the second key state variable, where the low-frequency compensator is used to suppress low-frequency oscillation;

[0011] The high-frequency compensator and the low-frequency compensator are integrated into the control system of the first voltage source converter, and the high-frequency compensator and the low-frequency compensator are integrated into the control system of the second voltage source converter. The control system of the first voltage source converter and the control system of the second voltage source converter belong to a back-to-back high-voltage DC system.

[0012] 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 common connection point voltage. The inner loop current control unit is used to adjust 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 power grid. The voltage source converter is the first voltage source converter or the second voltage source converter. The AC power grid is the AC power grid on the first voltage source converter side or the AC power grid on the second voltage source converter side. The small signal model is:

[0013] ;

[0014] in, 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 state variables included are 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 of the common connection point, represents the q-axis voltage component of the common connection point, represents the d-axis voltage component on the AC grid side, represents the q-axis voltage component on the AC grid side, represents the phase angle of the phase-locked loop, The angular frequency represents the phase angle of the phase-locked loop, represents the DC bus voltage, and the common connection point is the connection point between the voltage source converter and the AC grid;

[0015] Among them, the first key state variable that dominates the high-frequency oscillation in the small signal model is determined by participating in factor analysis, including:

[0016] Take partial derivatives of the state vector to obtain the values ​​of each element of the characteristic matrix;

[0017] 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 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.

[0018] For each high-frequency eigenvalue corresponding to the high-frequency mode, the first participation factors corresponding to each high-frequency eigenvalue are determined according to the right eigenvector and the left eigenvector corresponding to each high-frequency eigenvalue. The first participation factors are used to describe the contribution of the state variable to the high-frequency eigenvalue.

[0019] Normalizing each first participation factor corresponding to each high-frequency eigenvalue to obtain each normalized first participation factor;

[0020] The state variables corresponding to the normalized first participation factors corresponding to each high-frequency eigenvalue and greater than the first threshold are determined as the first key state variables that dominate the high-frequency oscillation.

[0021] In a feasible design, the second key state variable that dominates the low-frequency oscillation in the small signal model is determined by participating in factor analysis, including:

[0022] Acquire at least one preset variable, where the preset variable is a DC voltage proportional-integral controller transfer function of an outer loop control unit, a common connection point proportional-integral controller transfer function, or a proportional-integral controller transfer function of a phase-locked loop unit;

[0023] Adding at least one preset variable to the state vector to obtain a new state vector;

[0024] Calculate the partial derivative of the new state vector to obtain the values ​​of each element of the characteristic matrix;

[0025] 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.

[0026] For each low-frequency eigenvalue corresponding to the low-frequency mode, determine the second participation factors corresponding to each low-frequency eigenvalue according to the right eigenvector and the left eigenvector corresponding to each low-frequency eigenvalue, where the second participation factors are used to describe the contribution of the state variable or the preset variable to the low-frequency eigenvalue;

[0027] Normalizing each second participation factor corresponding to each low-frequency eigenvalue to obtain each normalized second participation factor;

[0028] The variable corresponding to each normalized second participation factor greater than the second threshold corresponding to each low-frequency eigenvalue is determined as the second key state variable that dominates the low-frequency oscillation. The variable is a state variable or a preset variable.

[0029] In a feasible design, the first key state variable includes a d-axis voltage component of the common connection point and a q-axis voltage component of the common connection point. Determining the high-frequency compensator according to the first key state variable includes:

[0030] The function of the high-frequency compensator is determined according to the first key state variable 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.

[0031] In one feasible design, the transfer function of the high-frequency compensator is:

[0032] ;

[0033] in, represents the transfer function of the high-frequency compensator, represents the gain of the high-frequency compensator, represents the complex variable parameter value, Indicates the cutoff frequency of the high-pass filter.

[0034] In a feasible design, the cutoff 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.

[0035] In a feasible design, the second key state variable includes the phase angle of the phase-locked loop, the DC bus voltage, and various preset variables. Determining the low-frequency compensator according to the second key state variable includes:

[0036] According to the second key state variable, 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, thereby realizing low-frequency oscillation suppression.

[0037] In one possible design, the transfer function of the low-frequency compensator is:

[0038] ;

[0039] in, represents the transfer function of the low-frequency compensator, represents the gain of the low-frequency compensator, represents the complex variable parameter value, Indicates the cutoff frequency of the low-pass filter.

[0040] In one possible design, the method includes:

[0041] Determining key short-circuit ratios corresponding to the first voltage source converter through trajectories of the eigenvalues ​​of the first voltage source converter, where the key short-circuit ratios are short-circuit ratios corresponding to the eigenvalues ​​located on the imaginary axis;

[0042] determining key short-circuit ratios corresponding to the second voltage source converter through trajectories of characteristic values ​​of the second voltage source converter;

[0043] 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 cutoff frequency of the filter corresponding to the first voltage source converter and the cutoff frequency of the filter corresponding to the second voltage source converter are determined respectively.

[0044] In a second aspect, a stability enhancement system for a back-to-back high voltage direct current system is provided, comprising:

[0045] a first voltage source converter, wherein the first voltage source converter adopts an active power control mode;

[0046] a second voltage source converter, wherein 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 via 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 via an inductor-capacitor filter;

[0047] a control system for a first voltage source converter, the control system of the first voltage source converter comprising an outer loop control unit, an inner loop current control unit, and a phase-locked loop unit, the outer loop control unit being used to control a DC voltage and a voltage at a common connection point, the inner loop current control unit being used to regulate a d-axis current and a q-axis current of the voltage source converter, and the phase-locked loop unit being used to synchronize the voltage source converter with an AC power grid;

[0048] a control system of a second voltage source converter, the control system of the second voltage source converter being the same as the control system of the first voltage source converter;

[0049] A high-frequency compensator, which is used to suppress high-frequency oscillations and is integrated into the control system of the first voltage source converter and the control system of the second voltage source converter;

[0050] A low-frequency compensator is used to suppress low-frequency oscillations and is integrated into the control system of the first voltage source converter and the control system of the second voltage source converter.

[0051] The present embodiment constructs a detailed small-signal model of a back-to-back HVDC system. A comprehensive stability analysis of the small-signal model is then performed using participating factor analysis. This identifies the dominant factors of high-frequency and low-frequency instability mechanisms, leading to a comprehensive and effective compensation method. This involves adding a multi-objective compensator (including both a high-frequency and a low-frequency compensator). In practical applications, the high-frequency compensator of this application suppresses 165Hz high-frequency oscillations by injecting a high-pass PCC voltage signal. The low-frequency compensator reduces overshoot by 82% by injecting a low-pass PLL angular frequency signal.

[0052] 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 renewable energy power generation is often located in remote areas, the local power grid may be in an extremely weak state of SCR=1, which limits the grid connection of renewable energy. At present, in order to maintain the stable operation of the system, a large number of complex compensation equipment need to be installed and special control strategies need to be adopted, which increases equipment investment and maintenance costs. However, the high-frequency compensator and low-frequency compensator proposed in this application have a simple architecture and do not require additional reinforcement of the power grid, but can enable the B2B HVDC system to efficiently transmit power between extremely weak power grids. For example, in remote areas or areas with weak power grid structures, it can reduce energy losses during the transmission process, improve the efficiency of power resource utilization, reduce transmission costs, increase power transmission volume, meet regional electricity demand, and promote economic development. Therefore, the present application solution can also effectively promote the long-distance transmission of new energy and ensure the stability of power supply in remote areas. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] In order to more clearly illustrate the technical solution of the present application, the following is a brief introduction to the drawings required for use in the embodiments. Obviously, for ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0054] Figure 1 This is a stability enhancement method applied to a back-to-back high voltage direct current system provided by an exemplary embodiment of the present application;

[0055] Figure 2 This is a schematic diagram of a back-to-back high-voltage direct current system structure provided by an exemplary embodiment of the present application;

[0056] Figure 3 This is another structural diagram of a back-to-back high-voltage direct current system provided by an exemplary embodiment of the present application;

[0057] Figure 4 This is a schematic diagram of a control system structure of a voltage source converter provided by an exemplary embodiment of the present application;

[0058] Figure 5 1 is a schematic diagram of different dq-axis coordinate systems provided by an exemplary embodiment of the present application;

[0059] Figure 6 This is a schematic diagram of characteristic value movement trajectories of a B2B HVDC system under different frequency modes when the rectifier of VSC1 is operating, provided by an exemplary embodiment of the present application;

[0060] Figure 7 This is a schematic diagram of characteristic value movement trajectories of a B2B HVDC system under different frequency modes when the inverter of VSC1 is operating, provided by an exemplary embodiment of the present application;

[0061] Figure 8 This is a schematic diagram of characteristic value movement trajectories of a B2B HVDC system under different frequency modes when the rectifier of VSC2 is operating, provided by an exemplary embodiment of the present application;

[0062] Figure 9 This is a schematic diagram of characteristic value movement trajectories of a B2B HVDC system under different frequency modes when the inverter of VSC2 is operating, provided by an exemplary embodiment of the present application;

[0063] Figure 10 This is a schematic diagram of a participation factor analysis result of different eigenvalues ​​corresponding to VSC2 provided by an exemplary embodiment of the present application;

[0064] Figure 11 This is a schematic diagram of a participation factor analysis result of different eigenvalues ​​corresponding to VSC1 provided by an exemplary embodiment of the present application;

[0065] Figure 12 This is a schematic diagram of the control system structure of a voltage source converter with a compensator added, provided by an exemplary embodiment of the present application. DETAILED DESCRIPTION

[0066] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0067] This application aims to conduct a comprehensive stability analysis of the B2B HVDC system by establishing a detailed system model, identify the root causes of different instability mechanisms, and propose effective compensation methods. The effectiveness of these methods is verified through simulation and real-time hardware-in-the-loop testing.

[0068] Figure 1 This is an example of a stability enhancement method for a back-to-back high voltage direct current system provided by an exemplary embodiment of the present application. Figure 1 As shown, the method includes:

[0069] S110, build a small signal model of a back-to-back HVDC system.

[0070] The back-to-back high-voltage DC system includes a first voltage source converter and a second voltage source converter, wherein 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 capacitors, 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 inductor-capacitor filters.

[0071] The back-to-back high-voltage DC system built in this application is combined with Figure 2 、 Figure 3 and Figure 4 An exemplary description is given.

[0072] like Figure 2 As shown, the constructed back-to-back high voltage direct current system includes a first voltage source converter VSC1 and a second voltage source converter VSC2, the DC sides of which are connected via capacitors, and VSC1 is connected to the first AC grid (i.e. Figure 2 The grid 1 shown is connected, and VSC2 is connected to the second AC grid (i.e. Figure 2 2) Connection to the grid shown. P in The input power (i.e., the power flowing into the VSC) reflects the situation of AC side power transmission to the VSC. 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 A positive value is used. In inverter mode, the VSC injects power into the AC grid. The calculated result still reflects the power flowing from the AC side to the VSC, but the power transfer direction is opposite to that in rectifier mode. Unless otherwise specified, "VSC" refers to either VSC1 or VSC2. VSC is a general term for both VSC1 and VSC2. P e It represents the output power (i.e., the power flowing out of the VSC), which can reflect the power output of the VSC to the outside. Its magnitude and direction also depend on the operating mode and working conditions of the VSC. Changes in its value will affect the stability of the DC bus voltage.

[0073] For VSC1 or VSC2, if Figure 3 As shown, the DC side is connected through capacitance The AC side is connected to the AC grid through an inductor capacitor (LC) filter. =57.6 , , represents the DC line current, Indicates the VSC terminal voltage (Terminal Voltage), Indicates the filter resistance, which can be 1.09 . Indicates the VSC side current, Indicates the active power at the Point of Common Coupling (PCC), Indicates the reactive power of PCC. Indicates the AC grid current of the Alternating Current System (AC System), Indicates the AC grid voltage, which can be 220 , represents the AC grid inductance, Indicates the AC grid resistance.

[0074] Based on the above-mentioned system, the AC side dynamic equations of each VSC can be expressed in the AC grid dq axis reference system as follows:

[0075] , formula (1);

[0076] in, represents the d-axis component of the VSC side current, The d-axis component of the instantaneous value of the VSC terminal voltage is represented by represents the d-axis component of the instantaneous value of the PCC voltage, represents the angular frequency of the AC grid, Represents an imaginary unit. represents the d-axis component of the AC grid-side current, Represents the d-axis component of the instantaneous value of the AC grid side voltage.

[0077] , formula (2);

[0078] in, represents the q-axis component of the VSC side current, The q-axis component representing 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 an imaginary unit. represents the q-axis component of the AC grid-side current, Represents the q-axis component of the instantaneous value of the AC grid side voltage.

[0079] The short circuit ratio (SCR) used to define the grid strength is defined as shown in the following formula (3):

[0080] , formula (3);

[0081] in, Indicates the short-circuit power of the PCC, in MVA (megavolt-ampere). The short-circuit power reflects the short-circuit current that the AC grid can provide during a short-circuit fault. The larger it is, the stronger the AC grid's ability to provide short-circuit current is, and the stronger the AC grid is. Conversely, the weaker the AC grid is. Indicates the rated power of the VSC. Indicates the instantaneous value of the AC grid voltage. Represents the equivalent impedance of the power grid.

[0082] Vector control is key to regulating grid-connected VSCs. The VSC control system architecture can be divided into an outer control loop (i.e., outer control unit), an inner control loop (i.e., inner current control unit), and a phase-locked loop (PLL). The outer control unit controls the DC voltage and PCC voltage. The inner current control unit regulates the d-axis and q-axis currents of the voltage source converter (VSC). The PLL synchronizes the VSC with the AC grid. The VSC is either the first VSC (i.e., VSC1) or the second VSC (i.e., VSC2), and the AC grid is either the AC grid on the first VSC side or the AC grid on the second VSC side. To ensure rapid current response, the bandwidth of the inner current control unit needs to be relatively large, but must be lower than the VSC switching frequency, typically around one-tenth of the switching frequency. Furthermore, to ensure the stability and robustness of cascade control, the bandwidth of the outer current control unit is typically designed to be 10% to 20% of the bandwidth of the inner current control unit.

[0083] like Figure 4 As shown, the DC voltage control mechanism of the outer loop control unit generates the reference current d-axis component of the VSC, which is recorded as This is done by setting the required DC bus voltage to a reference value Or active power set point This is done by comparing the actual values ​​with their respective values. The resulting error is then passed to the Proportional Integral (PI) controller.

[0084] For example, by adding a feedforward component To enhance the transient response of the DC bus voltage, the feedforward component can predict and compensate for dynamic changes in the system, thereby accelerating the adjustment speed of the DC bus voltage and maintaining the stability of the DC bus voltage.

[0085] For the DC bus voltage controlled VSC the reference current d-axis component It can be mathematically described by the following formula (4):

[0086] , formula (4);

[0087] in, Indicates the actual value of the DC link voltage, which can be 400 , represents a complex variable, The d-axis component representing the steady-state value of the PCC voltage, It represents the transfer function of the DC voltage PI controller, which can be (2720 +63360) / .

[0088] The d-axis component of the reference current of the VSC for active power control is It can be described mathematically using the following formula (5):

[0089] , formula (5);

[0090] in, represents the actual value of the active power set point, represents the active power PI controller transfer function.

[0091] The PCC voltage control mechanism uses a PI compensator to resolve 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):

[0092] , formula (6);

[0093] in, Indicates the reference value of the PCC voltage steady state value, represents the actual measured value of the PCC voltage steady-state value, Represents the transfer function of the PCC voltage PI controller, which can be (631849.32 ) / .

[0094] like Figure 4 As shown in Figure 1, the inner loop current control unit uses a PI compensator to adjust the dq axis current (i.e., d axis current and q axis current) of the VSC. In order to ensure independent control of active current and reactive current, a decoupling term ( and ). In addition, PCC voltage feedforward is used to mitigate potential voltage disturbances and ensure robust current control. Based on this, the d-axis component and q-axis component of the actual measured value of the steady-state value of the VSC terminal voltage are shown in the following formula (7):

[0095] , formula (7);

[0096] in, The d-axis component representing the actual measured value of the steady-state value of the VSC terminal voltage, The d-axis component representing the actual measured value of the VSC current, The transfer function of the PI compensator of the inner loop current control unit can be (28.8 +545) / , The d-axis component representing the actual measured value of the PCC voltage steady-state value, The q-axis component of the actual measured value of the VSC current is represented. The q-axis component representing the actual measured value of the steady-state value of the VSC terminal voltage, The q-axis component representing the actual measured value of the PCC voltage steady-state value.

[0097] 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 significantly affect the performance and stability of the VSC. Therefore, it is crucial to consider the PLL factor when analyzing the stability of a VSC connected to a weak grid. The PLL control unit uses a PI controller to adjust the q-axis component of the PCC voltage to zero and generate an angular frequency. The angular frequency is then integrated to generate the synchronization angle, as shown in the following equation (8).

[0098] , formula (8);

[0099] in, Indicates the synchronization angle of the PCC voltage, that is, the phase angle of the phase-locked loop, The transfer function of the PI controller of the phase-locked loop control unit can be (0.00093 +0.02457) / , Indicates the rated angular frequency, The d-axis component representing the actual measured value of the instantaneous value of the PCC voltage, Indicates finding the integral.

[0100] The B2B HVDC system involves two independent dq coordinate systems: the dq coordinate system of the grid and the dq coordinate system of the VSC. When the system is in steady state, the two coordinate systems are synchronized; however, when the system is subjected to transient disturbances, a phase deviation will occur between the two coordinate systems, such as Figure 5 This phase deviation can be attributed to the response time delay of the phase-locked loop. Figure 5 in represents the q-axis of the dq coordinate system of the VSC, Represents the d-axis of the dq coordinate system of the VSC. represents the q-axis of the dq coordinate system of the power 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. Figure 5 As shown, the relationship between the dq coordinate system can be expressed using the following formula (9):

[0101] , formula (9);

[0102] in, represents the variables in the converter dq reference frame, It is a variable in the dq reference coordinate system of the power grid; and is the complex factor used to implement the reference coordinate system transformation, Right now , It represents the synchronization angle of the grid voltage and is obtained by integrating the angular frequency of the grid voltage.

[0103] Based on the above system, in a feasible design, the small signal model constructed by this application based on 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, not only considering the fluctuation of the grid voltage, but also incorporating the influence of the converter control strategy, thereby fully reflecting the stability characteristics of the back-to-back HVDC system.

[0104] , formula (10);

[0105] in, 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 state variables included are 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 of the common connection point, represents the q-axis voltage component of the common connection point, represents the d-axis voltage component on the AC grid side, represents the q-axis voltage component on the AC grid side, represents the phase angle of the phase-locked loop, The angular frequency represents the phase angle of the phase-locked loop, Represents the DC bus voltage, and the common connection point is the connection point between the voltage source converter and the AC grid.

[0106] 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.

[0107] In this application, , , represents the characteristic matrix corresponding to VSC1, represents the characteristic matrix corresponding to VSC2, represents the input matrix corresponding to VSC1, Represents the input matrix corresponding to VSC2.

[0108] This application calculates the feature matrix The eigenvalue of The trajectory of the system is used to analyze the stability boundary of the system under different short circuit ratios (SCR) to assist in designing a more robust back-to-back HVDC system. The values ​​of each element of are obtained by taking partial derivatives of the state vector. , the stability criterion is when the real part When the damping ratio is greater than 0, the system is unstable. , 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 eigenvalue, the stability boundary of the system under different short circuit ratios (SCR) 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 imaginary part (vibration frequency) of the eigenvalue. When the SCR decreases, the stability margin of the system decreases, and the eigenvalue gradually approaches the imaginary axis (i.e. ), and finally enter the right half plane (RHP) and cause instability. At this point, the critical short circuit ratio of the system instability can be determined, that is, the critical short circuit ratio (CSCR). CSCR can be understood as the ratio of the short circuit ratio to the instability of the system. The SCR corresponding to the eigenvalue of , at this time the damping ratio of the system will be very small, which means that the vibration of the system will be difficult to attenuate and the stability will be extremely poor.

[0109] Figure 6 The effect of reducing the SCR of Grid 1 from 10 to 1 on the dominant characteristic values ​​of the B2B HVDC system under rectifier operation of VSC1 is shown. Figure 7 The figure shows the effect of reducing the SCR of Grid 1 from 10 to 1 on the dominant characteristic value of the B2BHVDC system under the inverter operation of VSC1. In general, as the SCR decreases, the stability margin of the system decreases, gradually leading to system instability. 、 is the eigenvalue corresponding to the High Frequency Mode (HFM), is the eigenvalue corresponding to the low frequency mode (LFM), is the characteristic value corresponding to the intermediate frequency mode. Frequencies greater than 100Hz are usually called high frequencies, frequencies less than 20Hz are called low frequencies, and frequencies between the two are called intermediate frequencies. It can be seen that with the change of SCR, and The instability threshold is reached at SCR values ​​of 2.2 and 1.4, respectively. At a lower SCR of 1.15, it shows instability. Figure 7 As shown in Figure 2, when the inverter of VSC1 is switched to operation, it can be seen that with the change of SCR, neither high-frequency nor low-frequency instability is manifested.

[0110] Figure 8 The effect of reducing the SCR of Grid 2 from 10 to 1 on the dominant characteristic values ​​of the B2B HVDC system under rectifier operation of VSC2 is shown. Figure 9The effect of reducing the SCR of Grid 2 from 10 to 1 on the dominant characteristic values ​​of the B2BHVDC system under inverter operation of VSC2 is shown. The results are similar to those observed for VSC1, especially the high-frequency and low-frequency modes that cause instability under rectifier operation. and The HFM shown 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 the AC system with the same parameters. Figure 9 in is the eigenvalue corresponding to the intermediate frequency mode, which enters an unstable state when the SCR is 1.05. Figure 9 The eigenvalue corresponding to LFM in the equation enters an unstable state when SCR is 1.

[0111] is the eigenvalue corresponding to the low-frequency mode, which shows instability when the SCR is 1.25. However, the eigenvalue corresponding to the low-frequency mode of VSC1 is It exhibits 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 VSC2, which uses DC bus voltage control, is more susceptible to instability in weak grid scenarios than VSC1, which uses power control. Therefore, by considering the stability differences under different VSC control modes (DC bus voltage control / active power control), it is possible to effectively identify and optimize unstable factors in back-to-back HVDC systems, effectively guiding solutions to enhance the stability of back-to-back HVDC systems. Based on this consideration, in one feasible design, the method includes:

[0112] Determining key short-circuit ratios corresponding to the first voltage source converter through trajectories of the eigenvalues ​​of the first voltage source converter, where the key short-circuit ratios are short-circuit ratios corresponding to the eigenvalues ​​located on the imaginary axis;

[0113] determining key short-circuit ratios corresponding to the second voltage source converter through trajectories of characteristic values ​​of the second voltage source converter;

[0114] 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 cutoff frequency of the filter corresponding to the first voltage source converter and the cutoff frequency of the filter corresponding to the second voltage source converter are determined respectively.

[0115] For example, by adding low-pass filters with different cutoff frequencies on the VSC side under different control modes, the stability enhancement effect of the system can be further optimized. That is, the cutoff frequency of the low-pass filter of VSC1 is designed to be low to deal with the instability that may occur under low SCR; and the cutoff frequency of the low-pass filter of VSC2 is designed to be higher than the cutoff frequency of the low-pass filter of VSC1 to fully deal with the instability that only occurs under high SCR. In this way, the filter parameters can be accurately designed based on 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 can also include monitoring the operating status of VSC1 and VSC2 and adjusting the filter parameters in real time to adapt to changes in the grid status, thereby ensuring that the back-to-back HVDC system always maintains good stability.

[0116] In summary, high-frequency oscillation and low-frequency oscillation are the dominant factors of instability in B2B HVDC systems.

[0117] S120 , determining a first key state variable that dominates high-frequency oscillations in the small signal model and a second key state variable that dominates low-frequency oscillations in the small signal model by means of a participating factor analysis method.

[0118] Based on the above small signal model, the first key state variable that dominates the high-frequency oscillation in the small signal model is determined by participating in factor analysis in the following way:

[0119] Take partial derivatives of the state vector to obtain the values ​​of each element of the characteristic matrix;

[0120] 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 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.

[0121] For each high-frequency eigenvalue corresponding to the high-frequency mode, the first participation factors corresponding to each high-frequency eigenvalue are determined according to the right eigenvector and the left eigenvector corresponding to each high-frequency eigenvalue. The first participation factors are used to describe the contribution of the state variable to the high-frequency eigenvalue.

[0122] Normalizing each first participation factor corresponding to each high-frequency eigenvalue to obtain each normalized first participation factor;

[0123] The state variables corresponding to the normalized first participation factors corresponding to each high-frequency eigenvalue and greater than the first threshold are determined as the first key state variables that dominate the high-frequency oscillation.

[0124] The first threshold can be set according to actual needs.

[0125] It should be understood that high-frequency oscillation refers to the system operating in an unstable state in a high-frequency mode, while low-frequency oscillation refers to the system operating in an unstable state in a low-frequency mode.

[0126] The above embodiment can be implemented through the following steps, which are described below using VSC2 as an example:

[0127] (1) Eigenvalue decomposition:

[0128] For the feature matrix Perform eigenvalue decomposition to obtain the eigenvalues ​​corresponding to the high-frequency mode and its corresponding right eigenvector and the left eigenvector ,in, .

[0129] The right eigenvector is used to describe the high-frequency mode of the state variable The left eigenvector is used to describe the high-frequency mode. Sensitivity to each state variable.

[0130] For each eigenvalue , which can be solved by solving the linear equations , and get the right eigenvector , represents the identity matrix. This can be solved by solving the linear equations , and get the left eigenvector , that is, the left eigenvector is the transpose of the right eigenvector.

[0131] (2) Calculation of participation factor

[0132] First participation factor Indicates the The state variable The contribution degree (or influence degree) of the eigenvalue is the right eigenvector Middle Quantity and the left eigenvector Middle Quantity The product of , as shown in the following formula (11):

[0133] , formula (11);

[0134] (3) Normalization: Normalize the first participation factors corresponding to each eigenvalue so that their sum is 1, as shown in the following formula (12):

[0135] , formula (12);

[0136] in, Represents the normalized , Indicates the The state variable The contribution of the eigenvalues, , Indicates the number of state variables.

[0137] (4) Determine the first key state variable

[0138] The state variables corresponding to the normalized first participation factors corresponding to each high-frequency eigenvalue and greater than the first threshold are determined as the first key state variables that dominate the high-frequency oscillation.

[0139] The first threshold is set according to actual needs, for example, the value can be 0.1.

[0140] In order to clarify the influence of each state variable on the eigenvalue, each normalized first participation factor can also be ranked.

[0141] After sorting and screening the normalized first participation factors of each high-frequency eigenvalue, the following is generated: Figure 10 shown 、 The corresponding normalized first participation factor histograms. It can be seen that the first key state variables of VSC2 include the state variables It should be noted that Figure 10 The "2" in the subscript of the participation factor corresponds to VSC2. Figure 11 The “1” in the subscript of the participation factor corresponds to VSC1.

[0142] right and The steps for conducting the participant factor analysis are as described in the above example and will not be repeated here.

[0143] For the determination method of the first key state variable of VSC1, please refer to the description of the first key state variable of VSC2, which will not be repeated here. Figure 11 shown 、 The corresponding histograms of the normalized first participation factors, the first key state variables of VSC1 include the state variables .

[0144] It should be noted that the main factors affecting the high-frequency mode of the system can be determined as part of the variables in the first key state variable according to requirements.

[0145] 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 modes, and the VSC controller does not affect these modes.

[0146] The above-described embodiment identifies the first key state variable that dominates high-frequency oscillations through eigenvalue decomposition and participation factor analysis. This first key state variable includes state variables that significantly influence the system's dynamic behavior in high-frequency mode, providing a clear target for the subsequent design of a high-frequency compensator. The calculation and normalization of the participation factor quantifies the contribution of each state variable to the high-frequency eigenvalue, clearly identifying which state variables are the dominant factors in high-frequency oscillations. Furthermore, by screening the normalized first participation factor (to a value greater than a first threshold), the selected first key state variable is ensured to have a high contribution, 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) operating in different control modes, and the first threshold can be adjusted according to specific application scenarios, enhancing the flexibility and universality of the method.

[0147] This application takes into account that when the DC bus voltage or PCC voltage fluctuates, it will affect the and , and the control parameters of the phase-locked loop determine the bandwidth, damping and steady-state accuracy of the control loop. If we only focus on the physical state variables (such as current, voltage, phase angle), the analysis of the low-frequency mode stability of the system is not comprehensive enough. In order to fully grasp the dominant factors affecting the low-frequency mode stability of the system, this application also adds the DC voltage proportional-integral controller transfer function of the outer loop control unit, the common connection point proportional-integral controller transfer function and the proportional-integral controller transfer function of the phase-locked loop unit as preset variables to the analysis, which can quantify their contribution to the low-frequency oscillation and avoid missing key influencing factors. Based on this, in a feasible design, the second key state variable that dominates the low-frequency oscillation in the small signal model is determined by participating in factor analysis in the following way:

[0148] Acquire at least one preset variable, where the preset variable is a DC voltage proportional-integral controller transfer function of an outer loop control unit, a common connection point proportional-integral controller transfer function, or a proportional-integral controller transfer function of a phase-locked loop unit;

[0149] Adding at least one preset variable to the state vector to obtain a new state vector;

[0150] Calculate the partial derivative of the new state vector to obtain the values ​​of each element of the characteristic matrix;

[0151] 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.

[0152] For each low-frequency eigenvalue corresponding to the low-frequency mode, determine the second participation factors corresponding to each low-frequency eigenvalue according to the right eigenvector and the left eigenvector corresponding to each low-frequency eigenvalue, where the second participation factors are used to describe the contribution of the state variable or the preset variable to the low-frequency eigenvalue;

[0153] Normalizing each second participation factor corresponding to each low-frequency eigenvalue to obtain each normalized second participation factor;

[0154] The variable corresponding to each normalized second participation factor greater than the second threshold corresponding to each low-frequency eigenvalue is determined as the second key state variable that dominates the low-frequency oscillation. The variable is a state variable or a preset variable.

[0155] The second threshold can be set according to actual needs.

[0156] For example, the preset variables obtained include the DC voltage proportional integral controller transfer function of the outer loop control unit , Common connection point proportional integral controller transfer function and the proportional-integral controller transfer function of the phase-locked loop unit . Add at least one preset variable to the state vector to obtain a new state vector include , , , Based on this, Represents the new state vector of VSC1, including , (ie VSC1 corresponds to ), (ie VSC1 corresponds to ), (ie VSC1 corresponds to ). Represents the new state vector of VSC2, including , , (That is, VSC2 corresponds to ), (That is, VSC2 corresponds to ), (That is, VSC2 corresponds to ). Then Find the partial derivative and get the characteristic matrix and Taking VSC2 as an example, the feature matrix Perform eigenvalue decomposition to obtain the eigenvalue corresponding to the low-frequency mode and its corresponding right eigenvector and the left eigenvector ,in, . Right eigenvector and the left eigenvector The calculation method of and Calculation method. In addition, the subsequent steps for calculating the second participation factor and normalizing the second participation factor refer to the relevant examples for the first participation factor and are not repeated here. Finally, the state variable corresponding to each normalized second participation factor corresponding to each low-frequency eigenvalue that is greater than the second threshold is determined as the second key state variable that dominates the low-frequency oscillation.

[0157] In order to clarify the influence of each state variable on the eigenvalue, the normalized second participation factors can also be ranked.

[0158] After sorting and screening the normalized first participation factors of each low-frequency eigenvalue, the following is generated: Figure 10 shown The corresponding normalized first participation factor histogram. It can be seen that the second key state variables of VSC2 include , 、 、 and The above participating factor analysis reveals that the DC bus voltage, external controller state and PLL state are the main factors of low-frequency mode.

[0159] For the determination method of the second key state variable of VSC1, please refer to the description of the second key state variable of VSC2, which will not be repeated here. Figure 11 shown The corresponding histograms of the normalized first participation factors, the second key state variables of VSC1 include the state variables 、 、 and .

[0160] It should be noted that the main factors affecting the low-frequency mode of the system can be determined as part of the variables in the second key state variable according to requirements.

[0161] It can be seen that the main factor affecting the system's low-frequency mode is the interaction between the PLL and the VSC outer loop control unit. Since the unfavorable interaction between the PLL and the VSC outer loop control unit is caused by a large PLL bandwidth, reducing the PLL bandwidth can, for example, mitigate low-frequency oscillations and improve overall system stability.

[0162] The above embodiment forms an expanded new state vector by adding at least one preset variable to the original state vector. Among them, at least one preset variable includes the DC voltage proportional integral controller transfer function of the outer loop control unit, the common connection point proportional integral controller transfer function and / or the proportional integral controller transfer function of the phase-locked loop unit. Based on the new state vector, through eigenvalue decomposition and participation factor analysis, it is possible to further determine which state variables have a greater impact on the low-frequency mode of the system, and obtain an accurate second key state variable. This method not only takes into account the original state variables, but also introduces 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 stability of the system and provide strong support for subsequent stability enhancement measures.

[0163] S130: Determine a high-frequency compensator according to the first key state variable.

[0164] Among them, the high-frequency compensator is used to suppress high-frequency oscillation.

[0165] In a feasible design, the first key state variable includes a d-axis voltage component of the common connection point and a q-axis voltage component of the common connection point. The high-frequency compensator is determined according to the first key state variable by:

[0166] The function of the high-frequency compensator is determined according to the first key state variable 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.

[0167] like Figure 12 As shown, two high-frequency compensators are required, and the locations for adding them 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 common connection point, and the other high-frequency compensator is used to extract the high-frequency component of the q-axis voltage component of the common connection point.

[0168] In the above example, the high-frequency compensator uses a high-pass filter to extract the frequency pattern of the PCC voltage oscillations and then embeds them into a stable closed-loop system, thereby mitigating these oscillations.

[0169] Participation factor analysis shows that the d-axis and q-axis voltage components at the common connection point are the main contributors to the high-frequency mode. This means that these variables contribute significantly to the system's high-frequency oscillations. Therefore, a high-frequency compensator designed for these key state variables can extract the high-frequency components from the PCC voltage. By feeding the high-frequency components of the PCC voltage back to the inner-loop current control unit, the reference values ​​of the VSC's d-axis and q-axis currents can be dynamically adjusted to offset the impact of high-frequency oscillations on the system, forming an active compensation mechanism. Furthermore, because the inner-loop current control unit has a high bandwidth and response speed, injecting the high-frequency components of the PCC voltage into the inner-loop current control unit can quickly respond to changes in the high-frequency components, thereby enhancing the high-frequency compensator's ability to mitigate oscillations.

[0170] In a feasible design, the transfer function of the high-frequency compensator is shown in the following formula (13):

[0171] , formula (13);

[0172] in, represents the transfer function of the high-frequency compensator, represents the gain of the high-frequency compensator, represents a complex variable, Indicates the cutoff frequency of the high-pass filter, which can be set to 500 rad / s.

[0173] In the above example, Used to improve high frequency damping, by adjusting Stabilize the system while meeting the stability margin requirements. For example, it can be set to 0.15 as required.

[0174] In a feasible design, the cutoff 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, which can avoid the transition band region of the filter and effectively reduce high-frequency oscillation.

[0175] The above embodiments are applicable to both VSC1 and VSC2.

[0176] S140: Determine a low-frequency compensator according to the second key state variable.

[0177] Among them, the low-frequency compensator is used to suppress low-frequency oscillation.

[0178] In a feasible design, the second key state variable includes the phase angle of the phase-locked loop, the DC bus voltage, and various preset variables. The low-frequency compensator is determined according to the second key state variable in the following manner:

[0179] According to the second key state variable, 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, thereby realizing low-frequency oscillation suppression.

[0180] Among them, the low-frequency compensator is added as follows Figure 12 shown.

[0181] The aforementioned participation factor analysis shows that the interaction between the PLL and the VSC outer-loop controller in weak grid conditions (low SCR) is the primary factor causing low-frequency oscillations. The compensation signal in the above example is equivalent to introducing virtual damping into the system, which reduces the energy accumulation of low-frequency oscillations and thus suppresses them.

[0182] In a feasible design, the transfer function of the low-frequency compensator is shown in the following formula (14):

[0183] , formula (14);

[0184] in, represents the transfer function of the low-frequency compensator, represents the gain of the low-frequency compensator, represents the complex variable parameter value, Indicates the cutoff frequency of the low-pass filter. Can be set to 1700, Can be set to 100rad / second.

[0185] The input of the low frequency compensator is the disturbance angular frequency , as shown in the following formula (15):

[0186] , formula (15);

[0187] It can be seen that the disturbance angular frequency is the difference between the two angular frequencies, which only includes the change in angular frequency but not the steady-state value.

[0188] In the above example, is a stabilizing gain used to improve low-frequency oscillation damping. The low-pass filter ensures that only the target low-frequency oscillation is injected into the VSC external control unit loop, providing active compensation for the VSC's external control unit loop. While reducing the PLL bandwidth can mitigate low-frequency oscillations, it may also slow the system's response to dynamic changes, thereby reducing the system's transient performance. In the above example, adding a low-frequency compensator can provide additional damping to suppress low-frequency oscillations without significantly affecting the system's dynamic response speed. Therefore, compared to reducing the PLL bandwidth, adding a low-frequency compensator can improve the system's transient response and robustness.

[0189] The above embodiments are applicable to both VSC1 and VSC2.

[0190] S150, integrating the high-frequency compensator and the low-frequency compensator into the control system of the first voltage source converter, and integrating the high-frequency compensator and the low-frequency compensator into the control system of the second voltage source converter.

[0191] The control system of the first voltage source converter and the control system of the second voltage source converter belong to a back-to-back high-voltage direct current system.

[0192] The locations for adding high-frequency compensators and low-frequency compensators are shown in 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 feedforward channel.

[0193] The embodiment of this application constructs a detailed small-signal model of a back-to-back HVDC system. A comprehensive stability analysis of the small-signal model is then performed using participating factor analysis. This identifies the dominant factors of the high-frequency and low-frequency instability mechanisms, thereby proposing a comprehensive and effective compensation method involving the addition of multi-objective compensators (including high-frequency and low-frequency compensators). In practical applications, the high-frequency compensator of this application can suppress high-frequency oscillations of 165 Hz by injecting a high-pass PCC voltage signal; the low-frequency compensator reduces overshoot by 82% by injecting a low-pass PLL angular frequency signal.

[0194] 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 renewable energy power generation is often located in remote areas, the local power grid may be in an extremely weak state of SCR=1, which limits the grid connection of renewable energy. At present, in order to maintain the stable operation of the system, a large number of complex compensation equipment need to be installed and special control strategies need to be adopted, which increases equipment investment and maintenance costs. However, the high-frequency compensator and low-frequency compensator proposed in this application have a simple architecture and do not require additional reinforcement of the power grid, but can enable the B2B HVDC system to efficiently transmit power between extremely weak power grids. For example, in remote areas or areas with weak power grid structures, it can reduce energy losses during the transmission process, improve the efficiency of power resource utilization, reduce transmission costs, increase power transmission volume, meet regional electricity demand, and promote economic development. Therefore, the present application solution can also effectively promote the long-distance transmission of new energy and ensure the stability of power supply in remote areas.

[0195] The present application also provides a stability enhancement system for a back-to-back high-voltage direct current system, comprising:

[0196] a first voltage source converter, wherein the first voltage source converter adopts an active power control mode;

[0197] a second voltage source converter, wherein 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 via 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 via an inductor-capacitor filter;

[0198] a control system for a first voltage source converter, the control system of the first voltage source converter comprising an outer loop control unit, an inner loop current control unit, and a phase-locked loop unit, the outer loop control unit being used to control a DC voltage and a voltage at a common connection point, the inner loop current control unit being used to regulate a d-axis current and a q-axis current of the voltage source converter, and the phase-locked loop unit being used to synchronize the voltage source converter with an AC power grid;

[0199] a control system of a second voltage source converter, the control system of the second voltage source converter being the same as the control system of the first voltage source converter;

[0200] A high-frequency compensator, which is used to suppress high-frequency oscillations and is integrated into the control system of the first voltage source converter and the control system of the second voltage source converter;

[0201] A low-frequency compensator is used to suppress low-frequency oscillations and is integrated into the control system of the first voltage source converter and the control system of the second voltage source converter.

[0202] In a feasible design, the function of the high-frequency compensator 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.

[0203] In one feasible design, the transfer function of the high-frequency compensator is:

[0204] ;

[0205] in, represents the transfer function of the high-frequency compensator, represents the gain of the high-frequency compensator, represents the complex variable parameter value, Indicates the cutoff frequency of the high-pass filter.

[0206] In a feasible design, the cutoff 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.

[0207] 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, thereby achieving low-frequency oscillation suppression.

[0208] In one possible design, the transfer function of the low-frequency compensator is:

[0209] ;

[0210] in, represents the transfer function of the low-frequency compensator, represents the gain of the low-frequency compensator, represents the complex variable parameter value, Indicates the cutoff frequency of the low-pass filter.

[0211] For other implementations and effects of the above system, please refer to the description in the embodiment of the method for enhancing stability of a back-to-back high voltage direct current system, which will not be repeated here.

[0212] The basic principles of the present application have been described above in conjunction with specific embodiments. However, it should be noted that the advantages, strengths, and effects mentioned in this application are merely illustrative and not restrictive, and it should not be assumed that these advantages, strengths, and effects are required of each embodiment of this application. In addition, the specific details disclosed above are merely illustrative and facilitating understanding, and are not restrictive. The above details do not limit this application to necessarily being implemented using the above specific details.

[0213] It should be understood that although the steps in the flowcharts of the accompanying drawings are shown in sequence as indicated by the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order restriction on the execution of these steps, and they 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, and 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 in turn or alternately with other steps or at least a portion of the sub-steps or stages of other steps.

[0214] The block diagrams of the devices, devices, equipment, and systems involved in this application are intended only as illustrative examples and are not intended to require or imply that they must be connected, arranged, or configured in the manner shown in the block diagrams. As will be appreciated by those skilled in the art, these devices, devices, equipment, and systems can be connected, arranged, or configured in any manner. Words such as "include," "comprise," "have," and the like are open-ended words, meaning "including but not limited to," and can be used interchangeably therewith. The words "or" and "and" used herein refer to the words "and / or" and can be used interchangeably therewith, unless the context clearly indicates otherwise. The word "such as" used herein refers to the phrase "such as but not limited to," and can be used interchangeably therewith.

[0215] It should also be noted that in the apparatus, device, and method of the present application, each component or each step can be decomposed and / or recombined, and such decomposition and / or recombination should be regarded as equivalent solutions of the present application.

[0216] 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. Therefore, the present application is not intended to be limited to the aspects shown herein, but rather to be accorded the widest scope consistent with the principles and novel features disclosed herein.

[0217] The above description has been provided for the purpose of illustration and description. Furthermore, this description is not intended to limit the embodiments of the present application to the forms disclosed herein. Although a number of example aspects and embodiments have been discussed above, those skilled in the art will recognize certain variations, modifications, alterations, additions, and sub-combinations thereof.

Claims

1. A stability enhancement method for a back-to-back high voltage direct current system, characterized in that: include: Constructing a small signal model of a back-to-back high-voltage direct current (HVDC) system, the back-to-back high-voltage direct current (HVDC) system comprising a first voltage source converter (VSC) and a second voltage source converter (VSC), wherein the first VSC adopts an active power control mode, the second VSC adopts a DC bus voltage control mode, the DC sides of the first VSC and the second VSC are connected via a capacitor, and the AC sides of the first VSC and the second VSC are both connected to an AC power grid via an inductor-capacitor filter. Determining, by means of a participating factor analysis, a first key state variable that dominates high-frequency oscillations in the small-signal model and a second key state variable that dominates low-frequency oscillations in the small-signal model; determining a high-frequency compensator according to the first key state variable, wherein the high-frequency compensator is used to suppress high-frequency oscillation; determining a low-frequency compensator according to the second key state variable, wherein the low-frequency compensator is used to suppress low-frequency oscillation; The high-frequency compensator and the low-frequency compensator are integrated into the control system of the first voltage source converter, and the high-frequency compensator and the low-frequency compensator are integrated into the control system of the second voltage source converter. The control system of the first voltage source converter and the control system of the second voltage source converter belong to the back-to-back high-voltage direct current system.

2. The method according to claim 1, characterized in that 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 common connection point voltage. The inner loop current control unit is used to adjust 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 power grid. The voltage source converter is the first voltage source converter or the second voltage source converter. The AC power grid is the AC power grid on the first voltage source converter side or the AC power grid on the second voltage source converter side. The small signal model is: ； in, 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 state variables included are 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 of the common connection point, represents the q-axis voltage component of the common connection point, represents the d-axis voltage component on the AC grid side, represents the q-axis voltage component on the AC grid side, represents the phase angle of the phase-locked loop, The angular frequency represents the phase angle of the phase-locked loop, represents the DC bus voltage, and the common connection point is the connection point between the voltage source converter and the AC grid; The method of determining the first key state variable that dominates the high-frequency oscillation in the small signal model by means of participating factor analysis includes: Taking partial derivatives of the state vector to obtain values ​​of each element of the characteristic matrix; Performing eigenvalue decomposition on the characteristic matrix to obtain eigenvalues ​​corresponding to different frequency modes, and right eigenvectors and left eigenvectors corresponding to each eigenvalue, wherein 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, the first participation factors corresponding to each high-frequency eigenvalue are determined according to the right eigenvector and the left eigenvector corresponding to each high-frequency eigenvalue. The first participation factors are used to describe the contribution of the state variable to the high-frequency eigenvalue. Normalizing each first participation factor corresponding to each high-frequency eigenvalue to obtain each normalized first participation factor; The state variables corresponding to the normalized first participation factors corresponding to each high-frequency eigenvalue and greater than the first threshold are determined as the first key state variables that dominate the high-frequency oscillation.

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

4. The method according to claim 2, characterized in that The first key state variable includes a d-axis voltage component of the common connection point and a q-axis voltage component of the common connection point. Determining a high-frequency compensator according to the first key state variable includes: The function of the high-frequency compensator determined according to the first key state variable 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, characterized in that The transfer function of the high-frequency compensator is: ； in, represents the transfer function of the high-frequency compensator, represents the gain of the high-frequency compensator, represents the complex variable parameter value, Indicates the cutoff frequency of the high-pass filter.

6. The method according to claim 5, characterized in that The cutoff frequency is set to half the frequency of the eigenvalue with the highest vibration frequency among the eigenvalues ​​corresponding to the high-frequency mode.

7. The method according to claim 3, characterized in that The second key state variable includes a phase angle of a phase-locked loop, a DC bus voltage, and various preset variables. Determining a low-frequency compensator according to the second key state variable includes: According to the second key state variable, 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, thereby realizing low-frequency oscillation suppression.

8. The method according to claim 7, characterized in that The transfer function of the low-frequency compensator is: ； in, represents the transfer function of the low-frequency compensator, represents the gain of the low-frequency compensator, represents the complex variable parameter value, Indicates the cutoff frequency of the low-pass filter.

9. The method according to any one of claims 2 to 8, characterized in that The method comprises: Determining key short-circuit ratios corresponding to the first voltage source converter through trajectories of the eigenvalues ​​of the first voltage source converter, where the key short-circuit ratios are short-circuit ratios corresponding to the eigenvalues ​​located on the imaginary axis; determining key short-circuit ratios corresponding to the second voltage source converter through trajectories of characteristic values ​​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 cutoff frequency of the filter corresponding to the first voltage source converter and the cutoff frequency of the filter corresponding to the second voltage source converter are determined respectively.

10. A stability enhancement system for a back-to-back high voltage direct current system, characterized in that: include: a first voltage source converter, wherein the first voltage source converter adopts an active power control mode; a second voltage source converter, wherein 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 via capacitors, and the AC sides of the first voltage source converter and the second voltage source converter are both connected to an AC power grid via an inductor-capacitor filter; a control system for a first voltage source converter, the control system of the first voltage source converter comprising an outer loop control unit, an inner loop current control unit, and a phase-locked loop unit, the outer loop control unit being configured to control a DC voltage and a voltage at a point of common connection, the inner loop current control unit being configured to regulate a d-axis current and a q-axis current of the voltage source converter, and the phase-locked loop unit being configured to synchronize the voltage source converter with an AC power grid; a control system of a second voltage source converter, the control system of the second voltage source converter being the same as the control system of the first voltage source converter; a high-frequency compensator, the high-frequency compensator being used to suppress high-frequency oscillations and being integrated into the control system of the first voltage source converter and the control system of the second voltage source converter; A low-frequency compensator is used to suppress low-frequency oscillations and is integrated into the control system of the first voltage source converter and the control system of the second voltage source converter, wherein the steps of determining the high-frequency compensator and the low-frequency compensator include: Constructing a small signal model of a back-to-back high voltage direct current (HVDC) system, the back-to-back high voltage direct current (HVDC) system comprising the first voltage source converter, the second voltage source converter, a control system of the first voltage source converter, and a control system of the second voltage source converter; Determining, by means of a participating factor analysis, a first key state variable that dominates high-frequency oscillations in the small-signal model and a second key state variable that dominates low-frequency oscillations in the small-signal model; determining the high frequency compensator according to the first key state variable; The low frequency compensator is determined according to the second key state variable.

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