VSG control method for oscillation instability

Abstract

The invention discloses a VSG control method for oscillation instability, and relates to the technical field of wind power control, and the method comprises the steps: determining the sequence impedance of a VSG grid-connected system according to a VSG inverter structure and a control circuit model; generating and analyzing a Bode diagram according to the sequence impedance of the VSG grid-connected system and the equivalent impedance of the power grids with different intensities to obtain a phase margin set; when at least one phase margin which is corresponding to the power grid intensity meeting the first preset condition and is a negative value exists, voltage and current tracking errors are calculated; calculating a current inner loop control rate according to a sliding mode surface function corresponding to the integral sliding mode surface, the voltage and current tracking errors and an exponential reaching law; when it is judged that the sliding mode surface function meets a second preset condition, an actual current measurement value is obtained; when the actual current measurement value does not conform to a third preset condition, the VSG grid-connected system sequence impedance is deduced again until no negative phase margin exists in the phase margin set; the steady-state error can be effectively eliminated, and the control performance is improved.

Description

Technical Field

[0001] The present application generally relates to the field of wind power control technology, and more specifically to a VSG control method for oscillation instability. Background Art

[0002] With the increasing share of renewable energy sources like wind power, wind power converters are trending from grid-following to grid-forming. This has made grid-forming converters a hot area of ​​research and application. Virtual synchronous generators (VSGs), as an important type of grid-forming converter, have attracted widespread attention due to their synchronous voltage source characteristics.

[0003] While VSGs exhibit certain advantages in weak grid environments, they present serious problems under strong grid conditions. Their dual-loop vector voltage and current control architecture exhibits significant flaws. As grid strength increases, the stability margin decreases, and the output impedance is extremely low at low frequencies, approaching zero, exhibiting capacitive characteristics. This characteristic results in insufficient phase margin at the intersection of the VSG's output impedance and the grid's inductive impedance at low frequencies in strong grid environments, easily leading to system oscillation and instability. This poses a significant threat to the safe and stable operation of the grid.

[0004] Currently, the primary method used for grid-connected converter stability analysis is impedance analysis. Impedance modeling for inverter-grid systems encompasses approaches such as dq coordinate system modeling and sequence impedance modeling. While some research has achieved some success in this area, such as establishing an impedance model for VSGs in the dq coordinate system and a sequence impedance model based on harmonic linearization, several challenges remain. For example, the impedance in the dq coordinate system is difficult to measure directly and its physical meaning is unclear. Furthermore, the sequence impedance model also has limitations in practical applications. Therefore, we propose a VSG control method for oscillatory instability to address these issues. Summary of the Invention

[0005] In view of the above-mentioned defects or deficiencies in the prior art, it is desired to provide a VSG control method for oscillation instability that enhances grid-connected stability under strong grid conditions.

[0006] The present application provides a VSG control method for oscillation instability, comprising the following steps: Determine the VSG grid-connected system sequence impedance based on the VSG inverter structure and control circuit model; the VSG grid-connected system sequence impedance includes positive sequence impedance and negative sequence impedance; Generating a Bode diagram based on the VSG grid-connected system sequence impedance and the equivalent impedances of grids of different strengths, and analyzing the Bode diagram based on the Nyquist stability criterion to obtain a phase margin set; the phase margin set includes a plurality of phase margins, and the phase margin is a difference between a phase and -180° at an intersection of the VSG grid-connected system sequence impedance and the equivalent impedance in the Bode diagram; When there is at least one phase margin in the phase margin set that corresponds to a grid strength that meets a first preset condition and is negative, calculating voltage and current tracking errors based on a current inner loop integral sliding mode controller of the VSG inverter structure and control circuit model; Constructing an integral sliding mode surface of the current inner loop integral sliding mode controller, and selecting an exponential reaching law based on the integral sliding mode surface; Calculating a current inner loop control rate based on a sliding surface function corresponding to the integral sliding surface, voltage and current tracking errors, and the exponential reaching law; The VSG inverter structure and control circuit model are driven to operate by utilizing the current inner loop control rate. If the operating state of the VSG inverter structure and control circuit model does not change and based on the Lyapunov function, it is determined that the sliding surface function meets the second preset condition, the actual current measurement value is obtained; and when the actual current measurement value does not meet the third preset condition, the VSG grid-connected system sequence impedance is re-derived until there is no negative phase margin in the phase margin set.

[0007] According to the technical solution provided in the embodiment of the present application, determining the sequence impedance of the VSG grid-connected system according to the VSG inverter structure and control circuit model specifically includes the following steps: Constructing a VSG inverter structure and control circuit model, and performing small disturbance component analysis on the output voltage and output current output by the VSG inverter structure and control circuit model to obtain small disturbance components of voltage and current frequency; According to the active and reactive power loops and the voltage and current control loops in the VSG inverter structure and control circuit model, the active and reactive power small signal components, the phase angle and reference voltage small disturbance components and the voltage reference value small disturbance components are obtained; Based on the KCL and KVL equations, the VSG grid-connected system sequence impedance is derived using the voltage and current frequency small disturbance components, the active and reactive power small signal components, the phase angle and reference voltage small disturbance components, and the voltage reference value small disturbance components.

[0008] According to the technical solution provided in the embodiment of the present application, the voltage and current frequency small disturbance components are calculated according to the following formula: ; in, is the voltage frequency small disturbance component, is the small disturbance component of current frequency, The frequency is The small perturbation component when The frequency is The small perturbation component when is the system reference frequency, is the steady-state component, is the phase angle corresponding to the positive sequence component, is the phase angle corresponding to the negative sequence component, is a small perturbation variable of the phase, is the complex imaginary unit; The small signal components of active and reactive power are calculated according to the following formula: ; in, is the small signal component of active power, is the reactive power small signal component, and are the small disturbance components of the voltage value of VSG in the grid-connected system in the dq coordinate system, and are the small disturbance components of the current value of VSG in the grid-connected system in the dq coordinate system, and are the steady-state components of the voltage value of VSG in the grid-connected system in the dq coordinate system, and are the steady-state components of the current value of VSG in the grid-connected system in the dq coordinate system, is the low-pass filter transfer function, is the low-pass filter cutoff frequency; The phase angle and the small disturbance component of the reference voltage are calculated according to the following formula: ; ; in, is the small perturbation component of the phase angle, is the small disturbance component of the reference voltage, is a complex frequency domain variable, is the active power transfer function, is the reactive transfer function, is the low-pass filter transfer function, is the moment of inertia, is the fundamental angular frequency, 、 are the active damping coefficient and the reactive damping coefficient, respectively. is the proportionality coefficient; The small disturbance component of the voltage reference value is calculated according to the following formula: ; in, and is the small disturbance component of the voltage reference value, , , and are the PI regulator transfer functions of the voltage and current control loops, , , 、 are the reference values ​​of the output voltage amplitude of the VSG power outer loop, 、 are the output current in dq coordinates, is the small disturbance component of the voltage in the dq coordinate system of the grid connection point.

[0009] According to the technical solution provided in the embodiment of the present application, the positive sequence impedance is calculated according to the following formula: ; in, is the positive sequence impedance, is the positive sequence voltage component, is the positive sequence current component, is the filter inductor, is the filter capacitor, is the filter resistor, 、 for 、 The corresponding angular frequency, is the current inner loop PI controller transfer function, is the voltage outer loop PI controller transfer function, 、 、 、 、 are characteristic polynomials, 、 are the proportional coefficients of the current loop and voltage loop respectively, 、 are the integral coefficients of the current loop and voltage loop respectively; Calculate the negative sequence impedance according to the following formula: .

[0010] According to the technical solution provided in the embodiment of the present application, the voltage and current tracking errors are calculated according to the following formula: ; in, is the voltage tracking error, is the current tracking error, 、 are the expected values ​​of voltage and current, respectively, is the steady-state component of the voltage value of the VSG in the grid-connected system in the dq coordinate system, is the steady-state component of the current value of the VSG in the grid-connected system in the dq coordinate system.

[0011] According to the technical solution provided in the embodiment of the present application, the sliding surface function corresponding to the integral sliding surface is: ; in, is the sliding surface function, is the gain coefficient of the sliding surface, is the current error signal, For time.

[0012] According to the technical solution provided in the embodiment of the present application, the current inner loop control rate is calculated according to the following formula: ; ; in, is the exponential reaching law, is the rate of change of the d-axis reference current, is the VSG output voltage, 、 、 They are the filter inductance, inductance parasitic resistance, and filter capacitance of the inverter LCL filter. is the gain coefficient of the sliding surface, is the current error signal, Output voltage of the current inner loop integral sliding mode control.

[0013] According to the technical solution provided in the embodiment of the present application, the first preset condition is that the short-circuit ratio is greater than 10; The short-circuit ratio is calculated according to the following formula: ; Among them, SCR is the short circuit ratio, is the rated power, is the rated phase effective value of the power grid, is the equivalent impedance of the power grid.

[0014] It can be seen from the above technical solution that this application has at least the following beneficial effects: The present application provides a VSG control method for oscillation instability, which includes: determining the VSG grid-connected system sequence impedance according to the VSG inverter structure and control circuit model; the VSG grid-connected system sequence impedance includes positive sequence impedance and negative sequence impedance; generating a Bode diagram according to the VSG grid-connected system sequence impedance and the equivalent impedance of power grids of different strengths, and analyzing the Bode diagram according to the Nyquist stability criterion to obtain a phase margin set; the phase margin set includes multiple phase margins, and the phase margin is the difference between the phase at the intersection of the VSG grid-connected system sequence impedance and the equivalent impedance in the Bode diagram and -180°; when there is at least one phase margin in the phase margin set that corresponds to a power grid strength that meets a first preset condition and is negative, based on the VSG inverter structure and control circuit The current inner loop integral sliding mode controller of the model is used to calculate the voltage and current tracking errors; the integral sliding mode surface of the current inner loop integral sliding mode controller is constructed, and the exponential reaching law is selected based on the integral sliding mode surface; the current inner loop control rate is calculated according to the sliding surface function, voltage and current tracking errors and exponential reaching law corresponding to the integral sliding mode surface; the current inner loop control rate is used to drive the VSG inverter structure and control circuit model to operate, and if the operating status of the VSG inverter structure and control circuit model does not change and based on the Lyapunov function, it is judged that the sliding surface function meets the second preset condition, the actual current measurement value is obtained; and when the actual current measurement value does not meet the third preset condition, the VSG grid-connected system sequence impedance is re-derived until there is no negative phase margin in the phase margin set.

[0015] This application constructs a VSG inverter structure and control circuit model to determine the sequence impedance, and generates a Bode diagram based on different grid equivalent impedances to analyze the phase margin, accurately locating system instability risk points. When a negative phase margin occurs, the current inner loop integral sliding mode controller is used to calculate the error, design the sliding mode surface, and use the reaching law to derive the control rate. The sequence impedance is then re-derived until the negative phase margin is eliminated. This effectively enhances the grid-connected stability of the VSG under strong grid conditions, reduces the risk of system oscillation and instability, and ensures safe and stable grid operation. Furthermore, compared to traditional control methods, this application utilizes an integral sliding mode controller and an exponential reaching law to more effectively eliminate steady-state errors and improve control performance, significantly promoting the innovative development of VSG control strategies. Furthermore, under grid conditions of varying strengths, this method can adapt the VSG to grid changes by analyzing the phase margin and adjusting the sequence impedance. Whether in weak or strong grids, it can dynamically optimize control parameters to ensure stable system operation, expanding the application scope of VSGs in complex grid environments and improving the reliability and compatibility of renewable energy power generation systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Other features, objects and advantages of the present application will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings.

[0017] Figure 1 Flowchart of the VSG control method for oscillation instability.

[0018] Figure 2 Flowchart for determining the sequence impedance of the VSG grid-connected system.

[0019] Figure 3 This is the VSG main circuit topology and control block diagram.

[0020] Figure 4 This is the A-phase equivalent small signal circuit diagram.

[0021] Figure 5 Bode diagram of VSG and equivalent impedance of power grids with different strengths.

[0022] Figure 6 This is the equivalent control block diagram with integral sliding film control.

[0023] Figure 7 This is the control block diagram of the inner loop of integral synovial control.

[0024] Figure 8 Impedance Bode diagram of the integral sliding mode control system. DETAILED DESCRIPTION

[0025] The present application will be further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely for the purpose of explaining the relevant invention and are not intended to limit the invention. It should also be noted that, for ease of description, only portions relevant to the invention are shown in the accompanying drawings.

[0026] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in this application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0027] To make the description of the following embodiments clear and concise, a brief introduction to the related technologies is first given: In power systems, the virtual synchronous generator (VSG) is an important grid-connected converter. The interaction between its output impedance and the grid impedance has a critical impact on system stability. The VSG utilizes a vector voltage-current dual closed-loop control architecture. At low frequencies, its output impedance exhibits capacitive characteristics and is extremely low, approaching zero. This characteristic is determined by its control strategy and circuit structure. Within a specific frequency range, the VSG's internal control links and component parameters result in this impedance. The power grid typically exhibits inductive impedance, caused by components such as inductance in the transmission line. At low frequencies, this inductive impedance affects connected devices, and its magnitude and characteristics depend on factors such as the grid structure and the length and parameters of the transmission line. When a VSG is connected to the grid, its output impedance interacts with the grid's inductive impedance. This interaction is particularly pronounced at low frequencies. Due to the capacitive nature of the VSG's output impedance and the inductive nature of the grid impedance, they intersect at certain frequencies, forming an intersection. Insufficient phase margin at this impedance intersection means that the system's stability at that frequency is poor, making it susceptible to external interference and oscillation. Such oscillations can amplify, causing dramatic fluctuations in system parameters like voltage and current, impacting the normal operation of other equipment in the grid and potentially triggering a chain reaction, posing a significant threat to the safe and stable operation of the entire grid. For example, they can lead to overloaded power equipment, misoperation of protective devices, and, in severe cases, widespread power outages.

[0028] In light of this, this application constructs a VSG inverter structure and control circuit model to determine the sequence impedance, and generates a Bode diagram based on different grid equivalent impedances to analyze the phase margin, accurately locating system instability risk points. When a negative phase margin occurs, a current inner-loop integral sliding mode controller is used to calculate the error, design the sliding mode surface, and use the reaching law to derive the control rate. The sequence impedance is then re-derived until the negative phase margin is eliminated. This effectively enhances the grid-connected stability of the VSG under strong grid conditions, reduces the risk of system oscillation instability, and ensures safe and stable grid operation. Furthermore, compared to traditional control methods, this application utilizes an integral sliding mode controller and an exponential reaching law to more effectively eliminate steady-state errors and improve control performance, significantly promoting the innovative development of VSG control strategies. Furthermore, under grid conditions of varying strengths, this method can adapt the VSG to grid changes by analyzing the phase margin and adjusting the sequence impedance. Whether in weak or strong grids, it can dynamically optimize control parameters to ensure stable system operation, expanding the application scope of the VSG in complex grid environments and improving the reliability and compatibility of renewable energy power generation systems.

[0029] In order to make the VSG control method for oscillation instability provided by the embodiment of the present application clearer and easier to understand, the method is described below with reference to the accompanying drawings. Figure 1As shown in FIG, this figure is a flow chart of a VSG control method for oscillation instability provided by an embodiment of the present application, the method comprising: S100. Determine the VSG grid-connected system sequence impedance based on the VSG inverter structure and control circuit model; the VSG grid-connected system sequence impedance includes positive sequence impedance and negative sequence impedance.

[0030] It should be noted that if Figure 2 As shown in FIG, according to the VSG inverter structure and control circuit model, the sequence impedance of the VSG grid-connected system is determined, which specifically includes the following steps: S101. Construct a VSG inverter structure and control circuit model, and perform small disturbance component analysis on the output voltage and output current output by the VSG inverter structure and control circuit model to obtain voltage and current frequency small disturbance components.

[0031] In actual wind power systems, the VSG, a grid-connected converter, consists of an inverter structure that includes circuit components such as filter inductors, capacitors, and resistors. The control circuitry involves the coordinated operation of an outer power loop and an inner voltage and current loop. The outer power loop simulates the power regulation characteristics of a synchronous generator, while the inner voltage and current loop precisely controls the output voltage and current. Accurately modeling these structures and circuits enables simulation of the electrical characteristics of the VSG during grid-connected operation.

[0032] Here, power system operation inevitably involves various minor disturbances. Small-disturbance component analysis of the voltage and current output by the VSG inverter structure and control circuit model accounts for these minor variations while maintaining steady-state system operation. Using appropriate mathematical methods, the small-disturbance components of the voltage and current frequencies are isolated. These small-disturbance components reflect the changes in voltage and current frequency when the system is subject to minor disturbances, providing critical data for subsequent analysis of system stability and dynamic characteristics.

[0033] The voltage and current frequency small disturbance components are calculated according to the following formula: ; in, is the voltage frequency small disturbance component, is the small disturbance component of current frequency, The frequency is The small perturbation component when The frequency is The small perturbation component when is the system reference frequency, is the steady-state component, is the phase angle corresponding to the positive sequence component, is the phase angle corresponding to the negative sequence component, is a small perturbation variable of the phase, is the complex imaginary unit.

[0034] S102. According to the active and reactive power loops and the voltage and current control loops in the VSG inverter structure and control circuit model, obtain active and reactive power small signal components, phase angle and reference voltage small disturbance components, and voltage reference value small disturbance components.

[0035] Here, active power determines the transmission and conversion of electrical energy, while reactive power affects voltage stability. By analyzing these two loops and combining the small perturbation components of voltage and current, we can obtain small signal components of active and reactive power. These components reflect the changes in active and reactive power under small perturbations. The voltage and current control loop ensures that the voltage and current output of the VSG meet grid connection requirements. Analyzing this loop reveals small perturbation components of the phase angle and reference voltage, as well as small perturbation components of the voltage reference value. Small perturbations of the phase angle affect power transmission and system synchronization, small perturbations of the reference voltage directly affect the output voltage quality, and small perturbations of the voltage reference value reflect the control loop's adjustment of the reference voltage.

[0036] The small signal components of active and reactive power are calculated according to the following formula: ; in, is the small signal component of active power, is the reactive power small signal component, and are the small disturbance components of the voltage value of VSG in the grid-connected system in the dq coordinate system, and are the small disturbance components of the current value of VSG in the grid-connected system in the dq coordinate system, and are the steady-state components of the voltage value of VSG in the grid-connected system in the dq coordinate system, and are the steady-state components of the current value of VSG in the grid-connected system in the dq coordinate system, is the low-pass filter transfer function, is the low-pass filter cutoff frequency; The phase angle and the small disturbance component of the reference voltage are calculated according to the following formula: ; ; in, is the small perturbation component of the phase angle, is the small disturbance component of the reference voltage, is a complex frequency domain variable, is the active power transfer function, is the reactive transfer function, is the low-pass filter transfer function, is the moment of inertia, is the fundamental angular frequency, 、 are the active damping coefficient and the reactive damping coefficient, respectively. is the proportionality coefficient; The small disturbance component of the voltage reference value is calculated according to the following formula: ; in, and is the small disturbance component of the voltage reference value, , , and are the PI regulator transfer functions of the voltage and current control loops, , , 、 are the reference values ​​of the output voltage amplitude of the VSG power outer loop, 、 are the output current in dq coordinates, is the small disturbance component of the voltage in the dq coordinate system of the grid connection point.

[0037] S103. Based on the KCL and KVL equations, the sequence impedance of the VSG grid-connected system is derived using the voltage and current frequency small disturbance components, the active and reactive power small signal components, the phase angle and reference voltage small disturbance components, and the voltage reference value small disturbance components.

[0038] Here, KCL (Kirchhoff's Current Law) and KVL (Kirchhoff's Voltage Law) are fundamental laws of circuit analysis. KCL is used to ensure the balance of node currents in a circuit, while KVL is used to ensure the conservation of loop voltage. When determining the sequence impedance of a VSG grid-connected system, the various small perturbation components obtained above are substituted into these two laws. By organizing and calculating these small perturbation components and considering the influence of circuit component parameters and control parameters, the sequence impedance of the VSG grid-connected system is ultimately derived. Sequence impedance, which reflects the system's resistance to signals of different frequencies, including positive and negative sequence impedance, is crucial for analyzing the system's stability, power transmission capacity, and interaction with the grid under different operating conditions. It serves as an important basis for subsequent system stability analysis and control strategy design.

[0039] According to the above small disturbance component solution formula and the equivalent small signal circuit diagram of phase A, write the KCL and KVL equations to calculate the positive sequence impedance: ; in, is the positive sequence impedance, is the positive sequence voltage component, is the positive sequence current component, is the filter inductor, is the filter capacitor, is the filter resistor, 、 for 、 The corresponding angular frequency, is the current inner loop PI controller transfer function, is the voltage outer loop PI controller transfer function, 、 、 、 、 are characteristic polynomials, 、 are the proportional coefficients of the current loop and voltage loop respectively, 、 are the integral coefficients of the current loop and voltage loop respectively; in addition, 、 、 、 、 、 The expressions are: ; ; ; ; ; ; in, is the lower inductance of the transmission line.

[0040] The above 、 、 、 、 、 、 、 The expressions are: ; in, is the cutoff frequency of the low-pass filter, Active power transfer function, Reactive transfer function.

[0041] The above 、 The expressions are: ; ; in, 、 They are the d-axis and q-axis current components of the filter inductor, 、 are the input d-axis and q-axis voltage components respectively.

[0042] Furthermore, according to the conversion relationship between positive and negative sequence impedances, the negative sequence impedance can be obtained: .

[0043] The above steps construct a VSG inverter structure and control circuit model with a traditional dual closed-loop control strategy, and consider the frequency coupling effect. By analyzing the small disturbance components of the output voltage and current of the VSG inverter structure and control circuit model after Park transformation, combined with the active and reactive power loops and the voltage and current control loops, according to the KCL and KVL equations, the positive and negative sequence impedances of the VSG inverter are derived, providing a basis for subsequent stability analysis.

[0044] S200. Generate a Bode diagram based on the sequence impedance of the VSG grid-connected system and the equivalent impedance of grids of different strengths, and analyze the Bode diagram based on the Nyquist stability criterion to obtain a phase margin set; the phase margin set includes multiple phase margins, and the phase margin is a difference between the phase at the intersection of the sequence impedance of the VSG grid-connected system and the equivalent impedance in the Bode diagram and -180°.

[0045] It's important to note that after obtaining the VSG grid-connected system sequence impedance, a Bode plot is generated based on the equivalent impedances of grids of varying strengths. Grids of varying strengths have varying equivalent impedances. For example, a strong grid has a relatively low equivalent impedance, while a weak grid has a relatively high equivalent impedance. A Bode plot can intuitively display how impedance varies with frequency, including both amplitude and phase information.

[0046] The Bode plot is analyzed based on the Nyquist stability criterion to determine system stability. In the Bode plot, the difference between the phase at the intersection of the VSG grid-connected system sequence impedance and the grid equivalent impedance and -180° is the phase margin. The phase margin set contains multiple phase margin values ​​that reflect the system's stability under different grid strengths. When the phase margin at the intersection of the VSG grid-connected system sequence impedance and the grid equivalent impedance on the Bode plot is negative, the system will lose stability and may cause oscillation instability. If the phase margin is positive, it indicates that the system has sufficient anti-interference capability. By analyzing the phase margin set, a comprehensive understanding of the system's stability under different frequencies and grid strengths can be obtained.

[0047] S300. When there is at least one negative phase margin corresponding to the grid strength that meets the first preset condition in the phase margin set, the voltage and current tracking errors are calculated based on the current inner loop integral sliding mode controller of the VSG inverter structure and control circuit model.

[0048] It should be noted that the power grid strength is measured by the system short circuit ratio (SCR), with the following settings: SCR below 2 is an extremely weak power grid, SCR below 10 is a weak power grid, and SCR above 10 is a strong power grid.

[0049] Here, the short-circuit ratio is calculated according to the following formula: ; Among them, SCR is the short circuit ratio, is the rated power, is the rated phase effective value of the power grid, is the equivalent impedance of the power grid.

[0050] When a phase margin in the phase margin set meets the first preset condition (i.e., the short-circuit ratio is greater than 10, indicating a strong grid condition) and is negative, it indicates that the system is at risk of oscillation instability. At this time, it is necessary to use the current inner loop integral sliding mode controller of the VSG inverter structure and control circuit model to calculate the voltage and current tracking errors.

[0051] The current inner loop integral sliding mode controller is highly robust and responds quickly to system disturbances. Tracking errors are calculated by defining the difference between the desired and actual voltage and current values. These voltage and current tracking errors serve as the basis for subsequent adjustments to the control strategy, aiming to keep the actual voltage and current as close to the desired values ​​as possible, thereby improving system stability and power quality.

[0052] Here, the voltage and current tracking errors are calculated according to the following formulas: ; in, is the voltage tracking error, is the current tracking error, 、 are the expected values ​​of voltage and current, respectively, is the steady-state component of the voltage value of the VSG in the grid-connected system in the dq coordinate system, is the steady-state component of the current value of the VSG in the grid-connected system in the dq coordinate system.

[0053] S400: Construct an integral sliding mode surface of a current inner loop integral sliding mode controller, and select an exponential reaching law based on the integral sliding mode surface.

[0054] It should be noted that, to further optimize the control effect, an integral sliding surface is constructed for the current inner loop integral sliding mode controller. The integral sliding surface is designed to eliminate the system's steady-state error. By integrating the current error signal, the controller can effectively compensate for the steady-state error during the tracking process. For example, when the system has some fixed interference factors that prevent the current from accurately tracking the expected value, the integral sliding surface can accumulate error information and adjust the control variable, gradually eliminating these errors. Furthermore, an exponential reaching law is selected based on the integral sliding surface. The exponential reaching law determines the speed and manner in which the system state approaches the sliding surface. By properly selecting the parameters of the exponential reaching law, the system can quickly adjust its state to the sliding surface while ensuring stability, improving the system's dynamic response performance and reducing oscillation and overshoot.

[0055] S500 , calculating the current inner loop control rate according to the sliding mode surface function corresponding to the integral sliding mode surface, the voltage and current tracking errors, and the exponential reaching law.

[0056] It should be noted that the sliding surface function describes the characteristics of the system in the sliding mode state and is interrelated with the tracking error and reaching law. During the calculation process, the sliding surface function, voltage, and current tracking errors are substituted into the formula of the exponential reaching law. After mathematical derivation and calculation, the current inner loop control rate, which can control the current inner loop, is obtained. Here, the current inner loop control rate is used to drive the inverter and adjust the output current so that the system current can quickly and accurately track the desired value, enhancing the system's resistance to oscillation instability and ensuring stable system operation.

[0057] For example, using the d-axis control loop as an example, we first define the voltage and current tracking errors and derive the relevant expressions based on the circuit equations. To eliminate steady-state errors, we construct an integral sliding mode surface and select an exponential reaching law to improve control performance. By taking the derivative of the integral sliding mode surface and combining it with the reaching law, we derive the current inner loop control rate.

[0058] After the orthogonal decomposition of the current inner loop, the controller design form and parameters of the d-axis component and the q-axis component are the same. Therefore, this paper takes the d-axis control loop as an example to design an integral sliding mode controller. First, the voltage and current tracking errors are given as: ; in, is the voltage tracking error, is the current tracking error, 、 are the expected values ​​of voltage and current, respectively, is the steady-state component of the voltage value of the VSG in the grid-connected system in the dq coordinate system, is the steady-state component of the current value of the VSG in the grid-connected system in the dq coordinate system.

[0059] According to the equivalent control block diagrams KCL and KVL, the following formula can be derived: ; in, 、 are the actual values ​​of VSG output voltage and output current respectively, 、 、 They are the filter inductor, inductor parasitic resistance, and filter capacitor of the inverter LCL filter respectively.

[0060] S600. Use the current inner loop control rate to drive the VSG inverter structure and control circuit model to operate. If the operating status of the VSG inverter structure and control circuit model does not change and based on the Lyapunov function, it is judged that the sliding surface function meets the second preset condition, obtain the actual current measurement value; and when the actual current measurement value does not meet the third preset condition, re-derive the VSG grid-connected system sequence impedance until there is no negative phase margin in the phase margin set.

[0061] It should be noted that the current inner loop control rate is used to drive the inverter, issuing instructions to the VSG inverter structure and control circuit model, adjusting the output current of the VSG inverter structure and control circuit model to make the actual current as close to the desired value as possible. In actual operation, when the system detects voltage and current tracking errors, the current inner loop control rate can be used to calculate the appropriate control signal to drive the inverter's power switching devices, thereby changing the output current magnitude and phase, achieving precise current control.

[0062] The second precondition is that the sliding surface function can approach zero within a finite time. The Lyapunov function is a mathematical tool used to analyze system stability. By performing Lyapunov analysis on the sliding surface function, it is possible to determine whether the system is stable and under what conditions it can remain stable.

[0063] While the VSG inverter is driven by the current inner loop control rate, the operating status of the VSG inverter structure and control circuit model must be monitored in real time. If the operating status remains unchanged and the sliding surface function, as determined by the Lyapunov function, meets the second pre-determined condition—that it approaches zero within a finite time—the system is in a stable convergence state. Specifically, when the sliding surface function approaches zero, the system is progressing toward its desired state, and actual current measurements can be obtained.

[0064] The third precondition states that the actual current measurement value can approach the expected value from the actual value within a finite time. After obtaining the actual current measurement value, it is necessary to determine whether it meets the third precondition, namely, that the actual current measurement value can approach the expected value from the actual value within a finite time. If this condition is met, it indicates that the current control strategy is effective and the current is moving in a stable direction. If not, the control strategy needs to be adjusted, that is, the sequence impedance of the VSG grid-connected system needs to be re-derived. By continuously re-deriving the sequence impedance and performing stability analysis again (such as generating a Bode plot and calculating the phase margin), until there are no negative phase margins in the phase margin set, the system can be ensured to operate stably under various operating conditions and effectively control VSG oscillation instability.

[0065] The purpose of re-deriving the sequence impedance is to analyze the stability of the system in its current state. By re-deriving the sequence impedance, the system's blocking characteristics for signals of different frequencies under the new operating state can be obtained. Then, a Bode plot is generated by combining the equivalent impedances of power grids of different strengths, and the phase margin is calculated according to the Nyquist stability criterion. As long as there are still negative phase margins in the phase margin set, it means that the system is still at risk of oscillation instability. It is necessary to continue to repeat the above steps, that is, use the new current inner loop control rate to drive the system operation, determine the system state, obtain current measurement values, re-derive the sequence impedance, etc., until there are no negative phase margins in the phase margin set, thereby ensuring that the system can operate stably under various operating conditions.

[0066] Furthermore, the sliding surface function corresponding to the integral sliding surface is: ; in, is the sliding surface function, is the gain coefficient of the sliding surface, is the current error signal, For time.

[0067] In order to improve the control effect and the sliding mode control performance, the exponential reaching law is selected as follows: ; in, 、 , for The sign function of .

[0068] right Find the first-order derivative, Substituting in: ; Finally, the joint and , derive the current inner loop control rate : .

[0069] Select the following Lyapunov function: ; Then Substituting the first-order derivative of the above formula, we get: ; in, , Can converge in a finite time, characterize It can approach 0 in a finite time. Under control, the current measurement value It can approach the expected value from the actual value in a limited time.

[0070] According to the above formula combined with the equivalent small signal circuit, KCL and KVL equations are written to solve the positive sequence impedance of the VSG using integral sliding mode control. as follows: ; in, is the filter inductor, is the filter capacitor, is the filter resistor, 、 for 、 The corresponding angular frequency. is the current inner loop PI controller transfer function, is the voltage outer loop PI controller transfer function, where is the gain coefficient of the sliding surface, Reaching law parameters is the proportional coefficient of the voltage loop, is the integral coefficient of the voltage loop.

[0071] The above 、 、 、 、 、 The expressions are: ; ; ; ; ; ; in, is the lower inductance of the transmission line.

[0072] The above 、 、 、 、 、 、 、 The expressions are: ; in, is the cutoff frequency of the low-pass filter, Active power transfer function, Reactive transfer function, 、 are the active transfer function and reactive transfer function after small signal linearization correction respectively.

[0073] The above 、 The expressions are: ; ; in, 、 are the d-axis and q-axis current components of the filter inductor respectively, 、 are the input d and q axis voltage components respectively.

[0074] Based on the aforementioned integral sliding mode controller design, the VSG positive-sequence impedance expression using integral sliding mode control was re-derived. Analysis shows that this solution significantly enhances the VSG's output impedance inductance in the low-frequency range, improves the phase in the capacitive region, and reduces the low-frequency capacitive region, thereby increasing the phase margin at the intersection with the grid impedance and effectively improving the grid-connected system stability margin. This demonstrates the principle behind the integral sliding mode control strategy's improvement of VSG grid-connected stability.

[0075] For ease of understanding, the VSG control method for oscillation instability in this application is introduced below with reference to specific examples.

[0076] like Figure 3 and Figure 4Figure 2 shows the inverter structure and control circuit for a virtual synchronous generator using a traditional dual-closed-loop control strategy. The main circuit includes a filter inductor, inductor parasitic resistance, filter capacitor, damping resistor, and transmission line equivalent impedance. These components work together to filter harmonics and suppress resonance, while simulating a realistic grid connection environment. The control loop consists of an outer power loop and an inner voltage and current loop. The outer power loop generates voltage amplitude reference values ​​and phase angles, replacing the phase-locked loop function. The inner voltage and current loop tracks the output current through dual closed-loop control. Figure 3 The presented structure provides a physical basis for subsequent sequence impedance modeling and stability analysis.

[0077] First, a VSG inverter structure and control circuit model is established that accounts for frequency coupling effects. This model deduces from small-disturbance components of voltage and current to positive- and negative-sequence impedances, incorporating both circuit and control parameters, providing a solid theoretical foundation for subsequent stability analysis. These impedance expressions can be used in subsequent stability analysis to determine system stability under different operating conditions using various stability criteria (such as the Nyquist criterion). This provides guidance for VSG inverter design and parameter adjustment, ensuring stable and reliable system operation under a wide range of operating conditions.

[0078] Secondly, if Figure 5 As shown, the dotted line represents the grid impedance characteristic curve, and the solid line represents the VSG positive sequence output impedance characteristic curve. In the simulation experiment, the grid equivalent inductance values ​​of 6.5mH (corresponding to the system short-circuit ratio SCR=7), 3mH (corresponding to SCR=15) and 2.4mH (corresponding to SCR=20) were selected to analyze the VSG grid-connected stability under different grid strengths. According to the Nyquist stability criterion, once the phase margin of the VSG output impedance and the grid impedance at the intersection is negative, the system will experience oscillation instability. Figure 5 It can be seen that when the grid impedance is 6.5mH (that is, SCR=7), the grid impedance and the VSG output impedance interact in the low-frequency band. The impedance amplitude characteristic curves of the two intersect at a frequency of 23Hz, and the phase margin at this intersection is 16°. This phase margin meets the stability condition, so the system will not oscillate or become unstable at this time.

[0079] However, as the grid strength gradually increases, when the grid impedance becomes 3mH (corresponding to SCR=15) and 2.4mH (corresponding to SCR=20), the frequencies corresponding to the intersection of the amplitude-frequency characteristic curves of the VSG output impedance and the grid impedance reach 33Hz and 38Hz, respectively. The phase margins at the corresponding intersections also become -9° and -35.5°, respectively. Since the phase margin is negative at this time, it no longer meets the stability conditions.

[0080] By analyzing the grid-connected stability of the VSG grid-connected system, taking SCR as the measure of grid strength, and utilizing the Nyquist stability criterion and Bode plot, the key causes of system instability can be identified. Based on the impact of changes in grid equivalent inductance on impedance interaction under different SCR values, the design direction of the control strategy can be clarified, which will help to design a more stable and reliable VSG grid-connected system control strategy and ensure that the system can operate stably under various grid strengths.

[0081] Finally, the design of the integral sliding mode control strategy is divided into two parts. The first is the design of an integral sliding mode controller for the inner current loop. While traditional PI control is employed for the outer voltage loop, innovations are made for the inner current loop, using the d-axis control loop as a representative example. First, voltage and current tracking errors are defined. Related expressions are derived from the circuit equations. An integral sliding mode surface is constructed to eliminate steady-state errors. An exponential reaching law is selected to improve performance. The control rate of the inner current loop is derived by derivatives and simultaneous equations. The Lyapunov function is also used to demonstrate system stability. The selection principles and influence of the sliding mode surface gain coefficient and reaching law parameters are detailed, ensuring that the measured current approaches the expected value within a finite time. The design forms and parameters of the d- and q-axis controllers are identical. The second part is the principle of improving system stability. Based on this integral sliding mode controller design, the expression for the positive-sequence impedance of the VSG using integral sliding mode control is re-derived. Analysis shows that this strategy significantly enhances the output impedance inductance of the VSG in the low-frequency range, improves the phase in the capacitive region, and reduces the low-frequency capacitive region. This, in turn, increases the phase margin at the intersection with the grid impedance, effectively improving the stability margin of the grid-connected system.

[0082] like Figure 6 As shown in the figure, while the voltage outer loop retains traditional PI control, the current inner loop adopts integral sliding mode control. By constructing an integral sliding mode surface and an exponential reaching law, rapid convergence of the current error and elimination of steady-state error are achieved. The control rate is derived by combining the sliding mode surface derivative with the reaching law, ensuring that the current measurement approaches the desired value within a finite time. This figure visually demonstrates how integral sliding mode control is integrated into the original dual-loop architecture, reshaping the dynamic characteristics of the current inner loop and enhancing the stability of the VSG under strong power grid conditions.

[0083] like Figure 7 As shown in the figure, it focuses on the details of the integral sliding mode controller in the current inner loop, including error calculation, sliding surface construction, reaching law module, control rate generation, and stability proof. The error between the input current reference and the actual current is processed by the integral sliding mode surface and exponential reaching law, and the output control voltage drives the inverter. The Lyapunov function verifies that the system state converges to the sliding mode surface within a finite time. This figure details the implementation logic of the integral sliding mode controller, providing a basis for parameter design. The effectiveness of the control strategy is ensured through stability proof.

[0084] like Figure 8 As shown in the figure, the output impedance inductance of the VSG with integral sliding mode control in the current inner loop is significantly enhanced in the low-frequency range, the amplitude-frequency characteristic curve moves upward, the phase in the capacitive region is significantly improved, and the capacitive region of the VSG output impedance amplitude-frequency curve in the low-frequency range is reduced. When the VSG converter is connected to the grid with an inductance value of 3mH (SCR=15), 1.5mH (SCR=30), and 0.75mH (SCR=60), the phase margins at the intersection of the grid equivalent impedance characteristic curve and the VSG output impedance characteristic curve are 78°, 72°, and 63°, respectively. The phase margins at the intersection are all positive. The integral sliding mode control effectively improves the stability margin of the grid-connected system. It is relatively smooth in the low-frequency band, and the amplitude change in the high-frequency band is relatively Figure 3 The paper explains that by designing an integral sliding mode control strategy, an innovative current inner loop is created based on the traditional PI control of the voltage outer loop. The integral sliding mode surface and the exponential reaching law are constructed to derive the control rate and verify the stability. The re-derivation of the positive sequence impedance shows that this strategy can improve the stability margin of the grid-connected system, providing theoretical support for the optimization of VSG inverters and stable grid connection.

[0085] The above description is merely a preferred embodiment of the present application and an illustration of the technical principles employed. Those skilled in the art should understand that the scope of the invention herein is not limited to the technical solutions formed by the specific combination of the above-mentioned technical features, but also encompasses other technical solutions formed by any combination of the above-mentioned technical features or their equivalents without departing from the inventive concept. For example, a technical solution formed by replacing the above-mentioned features with (but not limited to) technical features having similar functions disclosed in this application.

Claims

1. A VSG control method for oscillation instability, characterized in that: The following steps are involved: Determine the VSG grid-connected system sequence impedance based on the VSG inverter structure and control circuit model; the VSG grid-connected system sequence impedance includes positive sequence impedance and negative sequence impedance; Generating a Bode diagram based on the VSG grid-connected system sequence impedance and the equivalent impedances of grids of different strengths, and analyzing the Bode diagram based on the Nyquist stability criterion to obtain a phase margin set; the phase margin set includes a plurality of phase margins, and the phase margin is a difference between a phase and -180° at an intersection of the VSG grid-connected system sequence impedance and the equivalent impedance in the Bode diagram; When there is at least one phase margin in the phase margin set that corresponds to a grid strength that meets a first preset condition and is negative, calculating voltage and current tracking errors based on a current inner loop integral sliding mode controller of the VSG inverter structure and control circuit model; Constructing an integral sliding mode surface of the current inner loop integral sliding mode controller, and selecting an exponential reaching law based on the integral sliding mode surface; Calculating a current inner loop control rate based on a sliding mode surface function corresponding to the integral sliding mode surface, voltage and current tracking errors, and the exponential reaching law; The VSG inverter structure and control circuit model are driven to operate by utilizing the current inner loop control rate. If the operating state of the VSG inverter structure and control circuit model does not change and based on the Lyapunov function, it is determined that the sliding surface function meets the second preset condition, the actual current measurement value is obtained; and when the actual current measurement value does not meet the third preset condition, the VSG grid-connected system sequence impedance is re-derived until there is no negative phase margin in the phase margin set.

2. A VSG control method for oscillation instability according to claim 1, characterized in that: Determining the VSG grid-connected system sequence impedance based on the VSG inverter structure and control circuit model specifically includes the following steps: Constructing a VSG inverter structure and control circuit model, and performing small disturbance component analysis on the output voltage and output current output by the VSG inverter structure and control circuit model to obtain small disturbance components of voltage and current frequency; According to the active and reactive power loops and the voltage and current control loops in the VSG inverter structure and control circuit model, the active and reactive power small signal components, the phase angle and reference voltage small disturbance components and the voltage reference value small disturbance components are obtained; Based on the KCL and KVL equations, the VSG grid-connected system sequence impedance is derived using the voltage and current frequency small disturbance components, the active and reactive power small signal components, the phase angle and reference voltage small disturbance components, and the voltage reference value small disturbance components.

3. A VSG control method for oscillation instability according to claim 2, characterized in that: The voltage and current frequency small disturbance components are calculated according to the following formula: ； in, is the voltage frequency small disturbance component, is the small disturbance component of current frequency, The frequency is The small perturbation component when The frequency is The small perturbation component when is the system reference frequency, is the steady-state component, is the phase angle corresponding to the positive sequence component, is the phase angle corresponding to the negative sequence component, is a small perturbation variable of the phase, is the complex imaginary unit; The small signal components of active and reactive power are calculated according to the following formula: ； in, is the small signal component of active power, is the reactive power small signal component, and are the small disturbance components of the voltage value of VSG in the grid-connected system in the dq coordinate system, and are the small disturbance components of the current value of VSG in the grid-connected system in the dq coordinate system, and are the steady-state components of the voltage value of VSG in the grid-connected system in the dq coordinate system, and are the steady-state components of the current value of VSG in the grid-connected system in the dq coordinate system, is the low-pass filter transfer function, is the low-pass filter cutoff frequency; The phase angle and the small disturbance component of the reference voltage are calculated according to the following formula: ； ； in, is the small perturbation component of the phase angle, is the small disturbance component of the reference voltage, is a complex frequency domain variable, is the active power transfer function, is the reactive transfer function, is the low-pass filter transfer function, is the moment of inertia, is the fundamental angular frequency, 、 are the active damping coefficient and the reactive damping coefficient, respectively. is the proportionality coefficient; The small disturbance component of the voltage reference value is calculated according to the following formula: ； in, and is the small disturbance component of the voltage reference value, , , and are the PI regulator transfer functions of the voltage and current control loops, , , 、 are the reference values ​​of the output voltage amplitude of the VSG power outer loop, 、 are the output current in dq coordinates, is the small disturbance component of the voltage in the dq coordinate system of the grid connection point.

4. A VSG control method for oscillation instability according to claim 3, characterized in that: The positive sequence impedance is calculated according to the following formula: ； in, is the positive sequence impedance, is the positive sequence voltage component, is the positive sequence current component, is the filter inductor, is the filter capacitor, is the filter resistor, 、 for 、 The corresponding angular frequency, is the current inner loop PI controller transfer function, is the voltage outer loop PI controller transfer function, 、 、 、 、 are characteristic polynomials, 、 are the proportional coefficients of the current loop and voltage loop respectively, 、 are the integral coefficients of the current loop and voltage loop respectively; Calculate the negative sequence impedance according to the following formula: 。 5. A VSG control method for oscillation instability according to claim 1, characterized in that: The voltage and current tracking errors are calculated according to the following formulas: ； in, is the voltage tracking error, is the current tracking error, 、 are the expected values ​​of voltage and current, respectively, is the steady-state component of the voltage value of the VSG in the grid-connected system in the dq coordinate system, is the steady-state component of the current value of the VSG in the grid-connected system in the dq coordinate system.

6. A VSG control method for oscillation instability according to claim 1, characterized in that: The sliding surface function corresponding to the integral sliding surface is: ； in, is the sliding surface function, is the gain coefficient of the sliding surface, is the current error signal, For time.

7. A VSG control method for oscillation instability according to claim 6, characterized in that: The current inner loop control rate is calculated according to the following formula: ； ； in, is the exponential reaching law, is the rate of change of the d-axis reference current, is the VSG output voltage, 、 、 They are the filter inductance, inductance parasitic resistance, and filter capacitance of the inverter LCL filter. is the gain coefficient of the sliding surface, is the current error signal, Output voltage of the current inner loop integral sliding mode control.

8. A VSG control method for oscillation instability according to claim 1, characterized in that: The first preset condition is that the short circuit ratio is greater than 10; The short-circuit ratio is calculated according to the following formula: ； Among them, SCR is the short circuit ratio, is the rated power, is the rated phase effective value of the power grid, is the equivalent impedance of the power grid.

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