A VSG control method for oscillation instability

Abstract

This application discloses a VSG control method for oscillation instability, relating to the field of wind power control technology. The method includes: determining the sequence impedance of the VSG grid-connected system based on the VSG inverter structure and control circuit model; generating and analyzing Bode plots based on the sequence impedance of the VSG grid-connected system and the equivalent impedance of grids with different strengths to obtain a phase margin set; calculating voltage and current tracking errors when at least one negative phase margin corresponding to a grid strength that meets a first preset condition; calculating the current inner-loop control law based on the sliding surface function corresponding to the integral sliding surface, the voltage and current tracking errors, and the exponential reaching law; obtaining the actual measured value of the current when the sliding surface function meets a second preset condition; and re-deriving the sequence impedance of the VSG grid-connected system when the actual measured value of the current does not meet a third preset condition, until there are no negative phase margins in the phase margin set. This method effectively eliminates steady-state errors and improves control performance.

Description

Technical Field

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

[0002] With the increasing proportion of new energy power generation such as wind power, wind power converters are showing a technological development trend from grid-following to grid-connected types, making grid-connected converters a hot research and application area. Virtual Synchronous Generators (VSGs), as an important type of grid-connected converter, have attracted widespread attention due to their synchronous voltage source characteristics.

[0003] While VSG exhibits certain advantages in weak grid environments, it reveals serious problems under strong grid conditions. Its vector voltage-current dual closed-loop control architecture has significant flaws. As grid strength increases, the stability margin continuously decreases, and the output impedance becomes extremely low at low frequencies, approaching zero, and exhibiting capacitive characteristics. This characteristic means that in strong grid environments, when the VSG's output impedance interacts with the grid's inductive impedance at low frequencies, insufficient phase margin at the intersection point can easily trigger system oscillations and instability, posing a significant threat to the safe and stable operation of the grid.

[0004] Currently, the main method used for grid-connected converter stability analysis is impedance analysis, and impedance modeling for inverter grid-connected systems encompasses methods such as dq coordinate system modeling and sequence impedance modeling. Although some research has achieved certain results in this area, such as establishing the impedance model of VSG in the dq coordinate system and the sequence impedance model based on harmonic linearization, some problems still exist. For example, the impedance in the dq coordinate system is difficult to measure directly and its physical meaning is not clear enough, while the sequence impedance model also has certain limitations in practical applications. Therefore, we propose a VSG control method for oscillatory instability to solve the above problems. Summary of the Invention

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

[0006] This application provides a VSG control method for oscillatory instability, comprising the following steps:

[0007] Based on the VSG inverter structure and control circuit model, the sequence impedance of the VSG grid-connected system is determined; the sequence impedance of the VSG grid-connected system includes positive sequence impedance and negative sequence impedance.

[0008] Based on the sequence impedance of the VSG grid-connected system and the equivalent impedance of the grid at different strengths, a Bode plot is generated. The Bode plot is then analyzed according to the Nyquist stability criterion to obtain a phase margin set. The phase margin set includes multiple phase margins, and each phase margin is the difference between the phase and -180° at the intersection of the sequence impedance of the VSG grid-connected system and the equivalent impedance in the Bode plot.

[0009] 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 error is calculated by the current inner loop integral sliding mode controller based on the VSG inverter structure and control circuit model.

[0010] Construct the integral sliding surface of the current inner loop integral sliding mode controller, and select an exponential reaching law based on the integral sliding surface;

[0011] The current inner loop control law is calculated based on the sliding surface function corresponding to the integral sliding surface, the voltage and current tracking errors, and the exponential reaching law.

[0012] The VSG inverter structure and control circuit model is driven by the current inner loop control law. If the operating state of the VSG inverter structure and control circuit model does not change and the sliding surface function meets the second preset condition based on the Lyapunov function, the actual measured value of the current is obtained. If the actual measured value of the current does not meet the third preset condition, the sequence impedance of the VSG grid-connected system is re-derived until there is no negative phase margin in the phase margin set.

[0013] According to the technical solution provided in the embodiments of this application, the sequence impedance of the VSG grid-connected system is determined based on the VSG inverter structure and control circuit model, specifically including the following steps:

[0014] A VSG inverter structure and control circuit model is constructed, and small disturbance component analysis is performed on the output voltage and output current output by the VSG inverter structure and control circuit model to obtain the small disturbance components of voltage and current frequency.

[0015] Based on the active and reactive power loops and voltage and current control loops in the VSG inverter structure and control circuit model, the small signal components of active and reactive power, the small disturbance components of phase angle and reference voltage, and the small disturbance components of voltage reference value are obtained.

[0016] Based on the KCL and KVL equations, the sequence impedance of the VSG grid-connected system is derived by utilizing the small perturbation components of voltage and current frequencies, the small signal components of active and reactive power, the small perturbation components of phase angle and reference voltage, and the small perturbation components of voltage reference value.

[0017] According to the technical solution provided in the embodiments of this application, the small frequency perturbation components of voltage and current are calculated according to the following formula:

[0018] ;

[0019] in, This is a small disturbance component at the voltage frequency. For small disturbance components at the current frequency. For frequency Small perturbation components at time, For frequency Small perturbation components at time, It is the system reference frequency. For steady-state components, This is the phase angle corresponding to the positive sequence component. This is the phase angle corresponding to the negative sequence component. For small perturbation variables of phase, It is the imaginary unit of complex numbers;

[0020] Calculate the small-signal components of active and reactive power using the following formula:

[0021] ;

[0022] in, For active power small signal components, This refers to the small-signal component of reactive power. and These represent the small disturbance components of the VSG voltage value in the grid-connected system in the dq coordinate system. and These represent the small disturbance components of the VSG current value in the grid-connected system in the dq coordinate system. and These represent the steady-state components of the VSG voltage in the grid-connected system in the dq coordinate system. and These represent the steady-state components of the VSG current in the grid-connected system in the dq coordinate system. Let be the transfer function of the low-pass filter. This is the cutoff frequency of the low-pass filter;

[0023] Calculate the phase angle and small disturbance component of the reference voltage using the following formula:

[0024] ;

[0025] ;

[0026] in, For small phase angle perturbation components, For the small disturbance component of the reference voltage, For complex frequency domain variables, For the active power transfer function, For reactive power transfer function, Let be the transfer function of the low-pass filter. For rotational inertia, The fundamental angular frequency, , These are the active power damping coefficient and the reactive power damping coefficient, respectively. This is the proportionality coefficient;

[0027] The small disturbance component of the voltage reference value is calculated using the following formula:

[0028] ;

[0029] in, and For small disturbance components of the voltage reference value, , , and These are the transfer functions of the PI regulator in the voltage and current control loops, respectively. , , , These are the reference values ​​for the amplitude of the VSG power outer loop output voltage. , The output currents in the dq coordinate system are respectively. This represents the small voltage disturbance component in the dq coordinate system at the grid connection point.

[0030] According to the technical solution provided in the embodiments of this application, the positive sequence impedance is calculated using the following formula:

[0031] ;

[0032] in, It is a positive sequence impedance. It is the positive sequence voltage component. This is the positive sequence current component. For filtering inductors, For filtering capacitors, For filtering resistors, , for , The corresponding angular frequency, The transfer function for the current inner-loop PI controller. The transfer function for the voltage outer loop PI controller. , , , , All are characteristic polynomials. , These are the scaling factors for the current loop and the voltage loop, respectively. , These are the integral coefficients for the current loop and the voltage loop, respectively;

[0033] Calculate the negative sequence impedance using the following formula:

[0034] .

[0035] According to the technical solution provided in the embodiments of this application, the voltage and current tracking errors are calculated using the following formulas:

[0036] ;

[0037] in, For voltage tracking error, For current tracking error, , These are the expected values ​​of voltage and current, respectively. Let VSG be the steady-state component of the voltage value of the grid-connected system in the dq coordinate system. Let VSG be the steady-state component of the current value of the VSG in the grid-connected system in the dq coordinate system.

[0038] According to the technical solution provided in the embodiments of this application, the sliding surface function corresponding to the integral sliding surface is:

[0039] ;

[0040] in, For sliding surface functions, The gain coefficient of the sliding surface. This is the current error signal. For time.

[0041] According to the technical solution provided in the embodiments of this application, the current inner loop control rate is calculated using the following formula:

[0042] ;

[0043] ;

[0044] in, For exponential convergence law, The rate of change of the d-axis reference current. This is the output voltage of the VSG. , , These are the filter inductor, inductor parasitic resistance, and filter capacitor of the inverter's LCL filter. The gain coefficient of the sliding surface. This is the current error signal. Output voltage of current inner loop integral sliding mode control.

[0045] According to the technical solution provided in the embodiments of this application, the first preset condition is a short-circuit ratio greater than 10;

[0046] Calculate the short-circuit ratio using the following formula:

[0047] ;

[0048] Where SCR is the short-circuit ratio. Rated power, This is the effective value of the rated phase voltage of the power grid. This is the equivalent impedance of the power grid.

[0049] As can be seen from the above technical solution, this application has at least the following beneficial effects:

[0050] This application provides a VSG control method for oscillation instability, comprising: determining 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 plot based on the VSG grid-connected system sequence impedance and the equivalent impedance of the grid at different strengths, and analyzing the Bode plot 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 and -180° at the intersection of the VSG grid-connected system sequence impedance and the equivalent impedance in the Bode plot; when there is at least one negative phase margin corresponding to a grid strength that meets a first preset condition in the phase margin set, based on the VSG inverter structure and control circuit... The model employs an inner-loop integral sliding mode controller to calculate voltage and current tracking errors. An integral sliding surface for the inner-loop controller is constructed, and an exponential reaching law is selected based on this surface. The inner-loop control law is calculated based on the sliding surface function, voltage and current tracking errors, and the exponential reaching law. The inner-loop control law drives the VSG inverter structure and control circuit model. If the operating state of the VSG inverter structure and control circuit model remains unchanged and the sliding surface function meets the second preset condition based on the Lyapunov function, the actual current measurement value is obtained. If the actual current measurement value does not meet the third preset condition, the sequence impedance of the VSG grid-connected system is re-derived until there are no negative phase margins in the phase margin set.

[0051] This application determines the sequence impedance by constructing a VSG inverter structure and control circuit model, and analyzes the phase margin by generating Bode plots based on the equivalent impedance of different power grids, enabling precise location of system instability risk points. When a negative phase margin occurs, the control law is derived by calculating the error using an integral sliding mode controller with an inner current loop, designing the sliding surface and the reaching law, and re-deriving the sequence impedance until the negative phase margin is eliminated. This effectively enhances the grid-connected stability of the VSG under strong power grid conditions, reduces the risk of system oscillation and instability, and ensures the safe and stable operation of the power grid. Furthermore, compared with traditional control methods, this application uses an integral sliding mode controller and an exponential reaching law, which can more effectively eliminate steady-state errors and improve control performance, playing a significant role in promoting the innovative development of VSG control strategies. Moreover, under different power grid environments, this method can adapt the VSG to power grid changes by analyzing the phase margin and adjusting the sequence impedance. Whether in a weak or strong power grid, it can dynamically optimize control parameters to ensure stable system operation, expanding the application scope of VSG in complex power grid environments and improving the reliability and compatibility of new energy power generation systems. Attached Figure Description

[0052] Other features, objects, and advantages of this application will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings.

[0053] Figure 1 This is a flowchart of the VSG control method for oscillating instability.

[0054] Figure 2 A flowchart for determining the sequence impedance of a VSG grid-connected system.

[0055] Figure 3 This is the main circuit topology and control block diagram of VSG.

[0056] Figure 4 This is the equivalent small-signal circuit diagram for phase A.

[0057] Figure 5 Bode plots of VSG and equivalent impedances of power grids with different strengths.

[0058] Figure 6 This is the equivalent control block diagram containing integral sliding diaphragm control.

[0059] Figure 7 This is the control block diagram for the inner loop of the integral sliding diaphragm control.

[0060] Figure 8 The impedance Bode plot for the integral sliding mode control system. Detailed Implementation

[0061] The present application will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, only the parts relevant to the invention are shown in the accompanying drawings.

[0062] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0063] To ensure clarity and conciseness in the description of the following embodiments, a brief introduction to the related technologies is given first:

[0064] In power systems, the Virtual Synchronous Generator (VSG) is an important grid-connected converter. The interaction between its output impedance characteristics and the grid impedance characteristics has a crucial impact on system stability. The VSG employs a vector voltage-current dual closed-loop control architecture. In the low-frequency range, its output impedance exhibits capacitive characteristics and is extremely low, approximately zero. This characteristic is determined by its control strategy and circuit structure. Within a specific frequency range, the internal control loops and component parameters of the VSG cause it to exhibit such impedance characteristics externally. The power grid typically possesses inductive impedance due to inductors and other components in transmission lines. In the low-frequency range, the inductive impedance of the grid affects connected equipment, the magnitude and characteristics of which depend on factors such as the grid structure, transmission line length, and parameters. When a VSG is connected to the grid, its output impedance interacts with the grid's inductive impedance. This interaction is particularly pronounced in the low-frequency range. Due to the capacitive nature of the VSG's output impedance and the inductive nature of the grid impedance, they intersect at certain frequency points, forming intersection points. At these impedance intersection points, insufficient phase margin indicates poor system stability at that frequency, making the system susceptible to external disturbances and prone to oscillations. Such oscillations can amplify over time, causing drastic fluctuations in system parameters such as voltage and current. This can affect the normal operation of other equipment in the power grid and may even trigger a chain reaction, posing a significant threat to the safe and stable operation of the entire power grid. For example, it may lead to overload of power equipment, malfunction of protection devices, and in severe cases, even large-scale power outages.

[0065] In view of this, this application determines the sequence impedance by constructing a VSG inverter structure and control circuit model, and analyzes the phase margin by generating Bode plots based on the equivalent impedance of different power grids, which can accurately locate the system instability risk points. When a negative phase margin occurs, the control law is obtained by calculating the error using the current inner-loop integral sliding mode controller, designing the sliding surface and the reaching law, and re-deriving the sequence impedance until the negative phase margin is eliminated. This effectively enhances the grid-connected stability of VSG under strong power grid conditions, reduces the risk of system oscillation and instability, and ensures the safe and stable operation of the power grid. Moreover, compared with traditional control methods, this application uses an integral sliding mode controller and an exponential reaching law, which can more effectively eliminate steady-state errors and improve control performance, playing an important role in promoting the innovative development of VSG control strategies. Furthermore, under different power grid environments, this method can enable VSG to adapt to power grid changes by analyzing the phase margin and adjusting the sequence impedance. Whether it is a weak or strong power grid, the control parameters can be dynamically optimized to ensure stable system operation, expanding the application scope of VSG in complex power grid environments and improving the reliability and compatibility of new energy power generation systems.

[0066] To make the VSG control method for oscillation instability provided in the embodiments of this application clearer and easier to understand, the method is described below with reference to the accompanying drawings. Figure 1 As shown, this figure is a flowchart of a VSG control method for oscillation instability provided in an embodiment of this application. The method includes:

[0067] S100. Based on the VSG inverter structure and control circuit model, determine the sequence impedance of the VSG grid-connected system; the sequence impedance of the VSG grid-connected system includes positive sequence impedance and negative sequence impedance.

[0068] It should be noted that, as Figure 2 As shown, based on the VSG inverter structure and control circuit model, the sequence impedance of the VSG grid-connected system is determined, specifically including the following steps:

[0069] 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 the small disturbance components of voltage and current frequency.

[0070] In practical wind power systems, the VSG, as a grid-connected converter, includes circuit components such as filter inductors, capacitors, and resistors in its inverter structure. The control circuit involves the coordinated operation of the power outer loop and the voltage-current inner loop. The power outer loop simulates the power regulation characteristics of a synchronous generator, while the voltage-current inner loop is responsible for precisely controlling the output voltage and current. By accurately modeling these structures and circuits, the electrical characteristics of the VSG during grid-connected operation can be simulated.

[0071] In the operation of a power system, various minor disturbances are unavoidable. Analyzing the small disturbance components of the voltage and current output from the VSG inverter structure and control circuit model involves considering these minute changes based on the system's steady-state operation. Using appropriate mathematical methods, the small disturbance components of the voltage and current frequencies are separated. These components reflect the changes in voltage and current frequencies when the system is subjected to minor disturbances, providing crucial data for subsequent analysis of system stability and dynamic characteristics.

[0072] Calculate the small frequency perturbation components of voltage and current using the following formulas:

[0073] ;

[0074] in, This is a small disturbance component at the voltage frequency. For small disturbance components at the current frequency. For frequency Small perturbation components at time, For frequency Small perturbation components at time, It is the system reference frequency. For steady-state components, This is the phase angle corresponding to the positive sequence component. This is the phase angle corresponding to the negative sequence component. For small perturbation variables of phase, It is the imaginary unit of complex numbers.

[0075] S102. Based on the active and reactive power loops and voltage and current control loops in the VSG inverter structure and control circuit model, obtain the small signal components of active and reactive power, the small disturbance components of phase angle and reference voltage, and the small disturbance components of voltage reference value.

[0076] 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 disturbance components of voltage and current, small-signal components of active and reactive power can be obtained. These components reflect the changes in active and reactive power under small disturbances. The voltage and current control loop ensures that the voltage and current output of the VSG meet grid connection requirements. Analyzing this loop yields small disturbance components of phase angle and reference voltage, as well as small disturbance components of voltage reference value. Small disturbances in phase angle affect power transmission and system synchronization, small disturbances in reference voltage directly relate to output voltage quality, and small disturbances in voltage reference value reflect the control loop's adjustment of the reference voltage.

[0077] Calculate the small-signal components of active and reactive power using the following formula:

[0078] ;

[0079] in, For active power small signal components, This refers to the small-signal component of reactive power. and These represent the small disturbance components of the VSG voltage value in the grid-connected system in the dq coordinate system. and These represent the small disturbance components of the VSG current value in the grid-connected system in the dq coordinate system. and These represent the steady-state components of the VSG voltage in the grid-connected system in the dq coordinate system. and These represent the steady-state components of the VSG current in the grid-connected system in the dq coordinate system. Let be the transfer function of the low-pass filter. This is the cutoff frequency of the low-pass filter;

[0080] Calculate the phase angle and small disturbance component of the reference voltage using the following formula:

[0081] ;

[0082] ;

[0083] in, For small phase angle perturbation components, For the small disturbance component of the reference voltage, For complex frequency domain variables, For the active power transfer function, For reactive power transfer function, Let be the transfer function of the low-pass filter. For rotational inertia, The fundamental angular frequency, , These are the active power damping coefficient and the reactive power damping coefficient, respectively. This is the proportionality coefficient;

[0084] The small disturbance component of the voltage reference value is calculated using the following formula:

[0085] ;

[0086] in, and For small disturbance components of the voltage reference value, , , and These are the transfer functions of the PI regulator in the voltage and current control loops, respectively. , , , These are the reference values ​​for the amplitude of the VSG power outer loop output voltage. , The output currents in the dq coordinate system are respectively. This represents the small voltage disturbance component in the dq coordinate system at the grid connection point.

[0087] S103. Based on the KCL and KVL equations, the sequence impedance of the VSG grid-connected system is derived by utilizing the small perturbation components of voltage and current frequency, the small signal components of active and reactive power, the small perturbation components of phase angle and reference voltage, and the small perturbation components of voltage reference value.

[0088] Here, Kirchhoff's Current Law (KCL) and Voltage Law (KVL) are fundamental laws for circuit analysis. KCL ensures the balance of node currents in the circuit, while KVL ensures the conservation of loop voltage. When determining the sequence impedance of a VSG grid-connected system, the various small disturbance components obtained above are substituted into these two laws. By organizing and calculating these small disturbance components, and considering the influence of circuit component parameters and control parameters, the sequence impedance of the VSG grid-connected system is finally derived. Using sequence impedance to reflect the system's impedance characteristics 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.

[0089] Based on the above formulas for solving small perturbation components and the equivalent small-signal circuit diagram of phase A, write the KCL and KVL equations to calculate the positive sequence impedance:

[0090] ;

[0091] in, It is a positive sequence impedance. It is the positive sequence voltage component. This is the positive sequence current component. For filtering inductors, For filtering capacitors, For filtering resistors, , for , The corresponding angular frequency, The transfer function for the current inner-loop PI controller. The transfer function for the voltage outer loop PI controller. , , , , All are characteristic polynomials. , These are the scaling factors for the current loop and the voltage loop, respectively. , These are the integral coefficients for the current loop and the voltage loop, respectively;

[0092] in addition, , , , , , The expressions are as follows:

[0093] ;

[0094] ;

[0095] ;

[0096] ;

[0097] ;

[0098] ;

[0099] in, Inductance for power transmission lines, etc.

[0100] The above , , , , , , , The expressions are as follows:

[0101] ;

[0102] in, This is the cutoff frequency of the low-pass filter. Active transfer function, Reactive power transfer function.

[0103] The above , The expressions are as follows:

[0104] ;

[0105] ;

[0106] in, , These are the d-axis and q-axis current components of the filter inductor, respectively. , These are the input d-axis and q-axis voltage components, respectively.

[0107] Furthermore, based on the conversion relationship between positive and negative sequence impedances, the negative sequence impedance can be obtained:

[0108] .

[0109] The above steps construct a VSG inverter structure and control circuit model based on 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, and combining the active and reactive power loops and voltage and current control loops, the positive and negative sequence impedances of the VSG inverter are derived based on the KCL and KVL equations, providing a foundation for subsequent stability analysis.

[0110] S200. Based on the sequence impedance of the VSG grid-connected system and the equivalent impedance of the grid at different strengths, a Bode plot is generated. The Bode plot is then analyzed according to the Nyquist stability criterion to obtain a phase margin set. The phase margin set includes multiple phase margins, which are the difference between the phase and -180° at the intersection of the sequence impedance and the equivalent impedance of the VSG grid-connected system in the Bode plot.

[0111] It should be noted that after obtaining the sequence impedance of the VSG grid-connected system, a Bode plot is generated by combining it with the equivalent impedance of grids of different strengths. Different grid strengths result in different equivalent impedances; for example, a strong grid has a relatively small equivalent impedance, while a weak grid has a relatively large equivalent impedance. The Bode plot can visually demonstrate how impedance changes with frequency, including amplitude and phase information.

[0112] Bode plots are analyzed using the Nyquist stability criterion to determine system stability. In the Bode plot, the phase margin is the difference between the phase at the intersection of the VSG grid-connected system sequence impedance and the grid equivalent impedance and -180°. The phase margin set contains multiple phase margin values, reflecting 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, it indicates that the system will lose stability and may experience oscillations and instability. If the phase margin is positive, it indicates that the system has sufficient anti-interference capability. By analyzing the phase margin set, the overall stability of the system under different frequencies and grid strengths can be obtained.

[0113] 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 error is calculated by the current inner loop integral sliding mode controller based on the VSG inverter structure and control circuit model.

[0114] It should be noted that the system short-circuit ratio (SCR) is used to measure the strength of the power grid. The following settings are used: an SCR of less than 2 is considered an extremely weak power grid, an SCR of less than 10 is considered a weak power grid, and an SCR of more than 10 is considered a strong power grid.

[0115] Here, the short-circuit ratio is calculated using the following formula:

[0116] ;

[0117] Where SCR is the short-circuit ratio. Rated power, This is the effective value of the rated phase voltage of the power grid. This is the equivalent impedance of the power grid.

[0118] When there is a negative phase margin in the phase margin set that meets the first preset condition (i.e., the short-circuit ratio is greater than 10, indicating a strong grid operating condition), it indicates that the system has the risk of oscillation and 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 error.

[0119] The current inner-loop integral sliding mode controller exhibits strong robustness and can respond quickly to system disturbances. Tracking errors are calculated by defining the differences between the expected and actual values ​​of voltage and current. These voltage and current tracking errors serve as the basis for subsequent adjustments to the control strategy, aiming to bring the actual voltage and current as close as possible to the expected values, thereby improving system stability and power quality.

[0120] Here, the voltage and current tracking errors are calculated according to the following formulas:

[0121] ;

[0122] in, For voltage tracking error, For current tracking error, , These are the expected values ​​of voltage and current, respectively. Let VSG be the steady-state component of the voltage value of the grid-connected system in the dq coordinate system. Let VSG be the steady-state component of the current value of the VSG in the grid-connected system in the dq coordinate system.

[0123] S400: Construct the integral sliding surface of the current inner loop integral sliding mode controller, and select the exponential reaching law based on the integral sliding surface.

[0124] It should be noted that, to further optimize the control effect, an integral sliding surface of the current inner-loop integral sliding mode controller is constructed. The design of the integral sliding surface is based on the consideration of eliminating the steady-state error of the system. By integrating the current error signal, the controller can effectively compensate for the steady-state error during tracking. For example, when there are some fixed disturbances in the system that cause the current to fail to accurately track the desired value, the integral sliding surface can accumulate error information and adjust the control quantity to gradually eliminate these errors. Furthermore, based on the integral sliding surface, an exponential reaching law is selected. The exponential reaching law determines the speed and manner in which the system state approaches the sliding surface. By reasonably selecting the parameters of the exponential reaching law, the system can quickly adjust its state to the sliding surface while ensuring stability, thereby improving the dynamic response performance of the system and reducing oscillations and overshoot.

[0125] S500: Based on the sliding surface function corresponding to the integral sliding surface, the voltage and current tracking errors, and the exponential reaching law, the current inner loop control law is calculated.

[0126] It should be noted that the sliding surface function describes the characteristics of the system in sliding mode, and it is related to the tracking error and the reaching law. In the calculation process, the sliding surface function, voltage, and current tracking errors are substituted into the formula of the exponential reaching law. Through mathematical derivation and calculation, the current inner loop control law that controls the current inner loop is obtained. Here, the current inner loop control law is used to drive the inverter, adjust the output current, so that the system current can quickly and accurately track the desired value, enhance the system's resistance to oscillations and instability, and ensure stable system operation.

[0127] For example, taking 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 surface and select an exponential reaching law to improve control performance. By differentiating the integral sliding surface and combining it with the reaching law, we derive the current inner-loop control law.

[0128] After orthogonal decomposition of the current inner loop, the controller design forms and parameters for the d-axis and q-axis components 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 follows:

[0129] ;

[0130] in, For voltage tracking error, For current tracking error, , These are the expected values ​​of voltage and current, respectively. Let VSG be the steady-state component of the voltage value of the grid-connected system in the dq coordinate system. Let VSG be the steady-state component of the current value of the VSG in the grid-connected system in the dq coordinate system.

[0131] Based on the equivalent control block diagrams KCL and KVL, the following formulas can be derived:

[0132] ;

[0133] in, , These are the actual values ​​of the VSG output voltage and output current, respectively. , , These are the filter inductor, inductor parasitic resistance, and filter capacitor of the inverter's LCL filter, respectively.

[0134] S600: Drive the VSG inverter structure and control circuit model using the current inner loop control law. If the operating state of the VSG inverter structure and control circuit model does not change and the sliding surface function meets the second preset condition based on the Lyapunov function, obtain the actual measured value of the current. When the actual measured value of the current does not meet the third preset condition, re-derive the sequence impedance of the VSG grid-connected system until there is no negative phase margin in the phase margin set.

[0135] It should be noted that the inner current loop control is used to drive the inverter, issuing commands to the VSG inverter structure and control circuit model to adjust the output current of the VSG inverter structure and control circuit model, so that the actual current is as close as possible to the desired value. In actual operation, when the system detects voltage and current tracking errors, the inner current loop control can calculate a suitable control signal to drive the inverter's power switching devices, thereby changing the magnitude and phase of the output current and achieving precise current control.

[0136] The second presupposition condition is that the sliding surface function can approach 0 in a finite amount of time. The Lyapunov function is a mathematical tool used to analyze the stability of a system. 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.

[0137] During the operation of the VSG inverter driven by the current inner loop control law, it is necessary to monitor the operating status of the VSG inverter structure and control circuit model in real time. If the operating status remains unchanged, and the sliding surface function meets the second preset condition based on the Lyapunov function (i.e., the sliding surface function can approach 0 within a finite time), it indicates that the system is in a stable convergent state. In other words, when the sliding surface function approaches 0, it means that the system state is developing in the ideal direction, and at this time, the actual current measurement value can be obtained.

[0138] The third pre-set condition refers to the actual measured current value approaching the expected value within a finite time. After obtaining the actual measured current value, it is necessary to determine whether it meets the third pre-set condition, i.e., the actual measured current value can approach the expected value within a finite time. If this condition is met, it indicates that the current control strategy has played a role, and the current is moving towards stability. If not, the control strategy needs to be adjusted, i.e., 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 Bode plots and calculating phase margins), until there are no negative phase margins in the phase margin set, the system can be ensured to operate stably under various operating conditions, achieving effective control of VSG oscillation instability.

[0139] The purpose of re-deriving the sequence impedance is to analyze the stability of the system under the current state. By re-deriving the sequence impedance, the system's impedance characteristics to signals of different frequencies under the new operating state can be obtained. Then, Bode plots are generated by combining the equivalent impedances of power grids with different strengths, and the phase margin is calculated according to the Nyquist stability criterion. As long as there are negative phase margins in the phase margin set, it indicates that the system still has the risk of oscillation and instability. The above steps need to be repeated, namely, driving the system operation with the new current inner loop control law, judging the system state, obtaining current measurement values, and re-deriving the sequence impedance, until there are no negative phase margins in the phase margin set, thereby ensuring that the system can operate stably under various operating conditions.

[0140] Furthermore, the sliding surface function corresponding to the integral sliding surface is:

[0141] ;

[0142] in, For sliding surface functions, The gain coefficient of the sliding surface. This is the current error signal. For time.

[0143] To improve control effectiveness and sliding mode control performance, the exponential reaching law selected is:

[0144] ;

[0145] in, , , for The symbolic function.

[0146] right Find the first derivative, and Substituting, we get:

[0147] ;

[0148] Finally, Lianli and The current inner loop control rate is derived. :

[0149] .

[0150] Choose the following Lyapunov functions:

[0151] ;

[0152] Then Substituting the first derivative of the above equation, we get:

[0153] ;

[0154] in, , It can converge in a finite time, representing It can approach 0 within a finite time. (In the controller) Under control, current measurement value It can approach the expected value from the actual value within a limited time.

[0155] Based on the above formulas and the equivalent small-signal circuit, the KCL and KVL equations are written and solved to obtain the positive-sequence impedance of the VSG using integral sliding mode control. as follows:

[0156] ;

[0157] in, For filtering inductors, For filtering capacitors, For filtering resistors, , for , The corresponding angular frequency. The transfer function for the current inner-loop PI controller. Here is the transfer function for the voltage outer loop PI controller, where The gain coefficient of the sliding surface. Approach Law Parameters It is the proportional coefficient of the voltage loop. It is the integral coefficient of the voltage loop.

[0158] The above , , , , , The expressions are as follows:

[0159] ;

[0160] ;

[0161] ;

[0162] ;

[0163] ;

[0164] ;

[0165] in, Inductance for power transmission lines, etc.

[0166] The above , , , , , , , The expressions are as follows:

[0167] ;

[0168] in, This is the cutoff frequency of the low-pass filter. Active transfer function, Reactive power transfer function , These are the active power transfer function and reactive power transfer function after small-signal linearization correction, respectively.

[0169] The above , The expressions are as follows:

[0170] ;

[0171] ;

[0172] in, , These are the d-axis and q-axis current components of the filter inductor, respectively. , These are the input d-axis and q-axis voltage components, respectively.

[0173] Based on the above integral sliding mode controller design, the positive-sequence impedance expression of the VSG using integral sliding mode control is re-derived. Analysis shows that this scheme significantly enhances the output impedance inductiveity of the VSG in the low-frequency range, increases the phase in the capacitive region, and reduces the low-frequency capacitive region, thereby improving the phase margin at the intersection with the grid impedance and effectively enhancing the stability margin of the grid-connected system. This demonstrates, in principle, the role of integral sliding mode control strategy in improving the grid-connected stability of the VSG.

[0174] To facilitate understanding, the VSG control method for oscillation instability in this application will be introduced below with specific examples.

[0175] like Figure 3 and Figure 4 As shown, this diagram illustrates the inverter structure and control circuit of a virtual synchronous generator under a traditional dual-loop control strategy. The main circuit includes a filter inductor, inductor parasitic resistance, filter capacitor, damping resistor, and the equivalent impedance of the transmission line. These components work together to filter harmonics and suppress resonance, while simulating a real power grid connection environment. The control loop is divided into a power outer loop and a voltage / current inner loop: the power outer loop generates voltage amplitude reference values ​​and phase angles, thus replacing the function of the phase-locked loop; the voltage / current inner loop tracks the output current through dual-loop control. Figure 3 The structure shown provides a physical basis for subsequent impedance modeling and stability analysis.

[0176] First, a VSG inverter structure and control circuit model considering frequency coupling effects is established. This model encompasses the derivation of small perturbation components of voltage and current to positive and negative sequence impedances, incorporating both circuit and control parameters, thus providing a solid theoretical foundation for subsequent stability analysis. In the subsequent stability analysis, these impedance expressions can be used to determine the system's stability under different operating conditions using various stability criteria (such as the Nyquist criterion), thereby providing guidance for the design and parameter tuning of the VSG inverter and ensuring stable and reliable operation of the system under various operating conditions.

[0177] Secondly, such as Figure 5 As shown, the dashed line represents the grid impedance characteristic curve, and the solid line represents the VSG positive-sequence output impedance characteristic curve. In the simulation experiment, several different cases were selected with grid equivalent inductance values ​​of 6.5mH (corresponding to a system short-circuit ratio SCR=7), 3mH (corresponding to SCR=15), and 2.4mH (corresponding to SCR=20) to analyze the grid-connected stability of the VSG under different grid strengths. According to the Nyquist stability criterion, if the phase margin between the VSG output impedance and the grid impedance at the intersection point is negative, the system will experience oscillation and instability. Figure 5As can be seen, when the grid impedance is 6.5mH (i.e., SCR=7), the grid impedance and VSG output impedance interact in the low-frequency range. Their impedance amplitude characteristic curves intersect at the frequency of 23Hz, and the phase margin at this intersection point is 16°. This phase margin satisfies the stability condition, so the system will not experience oscillation instability at this time.

[0178] 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 condition.

[0179] By analyzing the grid connection stability of VSG grid-connected systems, using SCR as a measure of grid strength, and employing the Nyquist stability criterion and Bode plot, the key causes of system instability can be identified. Furthermore, based on the impact of changes in the equivalent inductance of the grid under different SCR values ​​on impedance interaction, the design direction of the control strategy can be clarified. This helps to design a more stable and reliable control strategy for VSG grid-connected systems, ensuring stable operation of the system under various grid strengths.

[0180] Finally, the design of the integral sliding mode control strategy is divided into two parts. The first is the design of the current inner loop integral sliding mode controller. Under the premise of using traditional PI control in the voltage outer loop, innovation is carried out on the current inner loop, with the d-axis control loop as a typical example. First, the voltage and current tracking errors are defined, and relevant expressions are derived by combining circuit equations. To eliminate steady-state errors, an integral sliding surface is constructed, and an exponential reaching law is selected to improve performance. The current inner loop control law is derived by derivatives and simultaneous equations. At the same time, the Lyapunov function is selected to prove the system stability. The selection principles and effects of the sliding surface gain coefficient and reaching law parameters are explained in detail to ensure that the current measurement value approaches the desired value within a finite time. The d-axis and q-axis controller designs are identical in form and parameters. The second is the principle of system stability improvement. Based on this integral sliding mode controller design, the positive sequence impedance expression of VSG using integral sliding mode control is re-derived. Analysis shows that this strategy can significantly enhance the output impedance inductance of VSG in the low-frequency range, increase the phase in the capacitive region, reduce the low-frequency capacitive region, and thus improve the phase margin at the intersection with the grid impedance, effectively improving the stability margin of the grid-connected system.

[0181] like Figure 6As shown, while retaining traditional PI control in the outer voltage loop, the inner current loop employs integral sliding mode control. By constructing an integral sliding surface and an exponential reaching law, rapid convergence of current errors and elimination of steady-state errors are achieved. The control law is derived by simultaneously applying the derivative of the sliding surface and the reaching law, ensuring that the measured current value approaches the desired value within a finite time. This figure visually illustrates how integral sliding mode control is embedded in the original dual-loop architecture, enhancing the stability of the VSG under strong power grid conditions by reshaping the dynamic characteristics of the inner current loop.

[0182] like Figure 7 As shown, this diagram focuses on the details of the integral sliding mode controller for the inner current loop, including error calculation, sliding surface construction, reaching law module, control law generation, and stability proof. The error between the input current reference value and the actual current generation is processed by the integral sliding surface and exponential reaching law, and then the output control voltage drives the inverter. The convergence of the system state to the sliding surface in a finite time is verified using a Lyapunov function. This figure reveals the implementation logic of the integral sliding mode controller in detail, providing a basis for parameter design, and ensuring the effectiveness of the control strategy through stability proof.

[0183] like Figure 8 As shown, the VSG with integral sliding mode control in the inner current loop exhibits significantly enhanced output impedance inductance in the low-frequency range, shifting the amplitude-frequency characteristic curve upwards. This significantly improves the phase in the capacitive region and reduces the capacitive region of the VSG output impedance amplitude-frequency curve in the low-frequency range. When the VSG converter is connected to a grid with inductance values ​​of 3mH (SCR=15), 1.5mH (SCR=30), and 0.75mH (SCR=60), the phase margins at the intersection points of the grid equivalent impedance characteristic curve and the VSG output impedance characteristic curve are 78°, 72°, and 63°, respectively. All phase margins at the intersection points are positive, indicating that integral sliding mode control effectively improves the stability margin of the grid-connected system. The current loop is relatively smooth in the low-frequency range, while the amplitude variation in the high-frequency range is relatively... Figure 3 The results are relatively smooth. This indicates that by designing an integral sliding mode control strategy, an innovative current inner loop is created based on the traditional PI control in the voltage outer loop. The integral sliding mode surface and the exponential reaching law are constructed to derive the control law and prove the stability. Furthermore, the re-derived positive sequence impedance shows that this strategy can improve the stability margin of the grid-connected system, providing theoretical support for the optimization and stable grid connection of VSG inverters.

[0184] The above description is merely a preferred embodiment of this application and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of the invention involved in this application is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the inventive concept. For example, technical solutions formed by substituting the above features with (but not limited to) technical features with similar functions disclosed in this application.

Claims

1. A VSG control method for oscillating instability, characterized in that, Includes the following steps: Based on the VSG inverter structure and control circuit model, the sequence impedance of the VSG grid-connected system is determined; the sequence impedance of the VSG grid-connected system includes positive sequence impedance and negative sequence impedance. Based on the sequence impedance of the VSG grid-connected system and the equivalent impedance of the grid at different strengths, a Bode plot is generated. The Bode plot is then analyzed according to the Nyquist stability criterion to obtain a phase margin set. The phase margin set includes multiple phase margins, and each phase margin is the difference between the phase and -180° at the intersection of the sequence impedance of the VSG grid-connected system and the equivalent impedance in the Bode plot. 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 error is calculated by the current inner loop integral sliding mode controller based on the VSG inverter structure and control circuit model. Construct the integral sliding surface of the current inner loop integral sliding mode controller, and select an exponential reaching law based on the integral sliding surface; The current inner loop control law is calculated based on the sliding surface function corresponding to the integral sliding surface, the voltage and current tracking errors, and the exponential reaching law. The VSG inverter structure and control circuit model is driven by the current inner loop control law. If the operating state of the VSG inverter structure and control circuit model does not change and the sliding surface function meets the second preset condition based on the Lyapunov function, the actual measured value of the current is obtained. If the actual measured value of the current does not meet the third preset condition, the sequence impedance of the VSG grid-connected system is re-derived until there is no negative phase margin in the phase margin set.

2. The VSG control method for oscillation instability according to claim 1, characterized in that, Based on the VSG inverter structure and control circuit model, the sequence impedance of the VSG grid-connected system is determined, specifically including the following steps: A VSG inverter structure and control circuit model is constructed, and small disturbance component analysis is performed on the output voltage and output current output by the VSG inverter structure and control circuit model to obtain the small disturbance components of voltage and current frequency. Based on the active and reactive power loops and voltage and current control loops in the VSG inverter structure and control circuit model, the small signal components of active and reactive power, the small disturbance components of phase angle and reference voltage, and the small disturbance components of voltage reference value are obtained. Based on the KCL and KVL equations, the sequence impedance of the VSG grid-connected system is derived by utilizing the small perturbation components of voltage and current frequencies, the small signal components of active and reactive power, the small perturbation components of phase angle and reference voltage, and the small perturbation components of voltage reference value.

3. The VSG control method for oscillation instability according to claim 2, characterized in that, Calculate the small frequency perturbation components of voltage and current using the following formulas: ； in, This is a small disturbance component at the voltage frequency. For small disturbance components at the current frequency. For frequency Small perturbation components at time, For frequency Small perturbation components at time, It is the system reference frequency. For steady-state components, This is the phase angle corresponding to the positive sequence component. This is the phase angle corresponding to the negative sequence component. For small perturbation variables of phase, It is the imaginary unit of complex numbers; Calculate the small-signal components of active and reactive power using the following formula: ； in, For active power small signal components, This refers to the small-signal component of reactive power. and These represent the small disturbance components of the VSG voltage value in the grid-connected system in the dq coordinate system. and These represent the small disturbance components of the VSG current value in the grid-connected system in the dq coordinate system. and These represent the steady-state components of the VSG voltage in the grid-connected system in the dq coordinate system. and These represent the steady-state components of the VSG current in the grid-connected system in the dq coordinate system. Let be the transfer function of the low-pass filter. This is the cutoff frequency of the low-pass filter; Calculate the phase angle and small disturbance component of the reference voltage using the following formula: ； ； in, For small phase angle perturbation components, For the small disturbance component of the reference voltage, For complex frequency domain variables, For the active power transfer function, For reactive power transfer function, Let be the transfer function of the low-pass filter. For rotational inertia, The fundamental angular frequency, , These are the active power damping coefficient and the reactive power damping coefficient, respectively. This is the proportionality coefficient; The small disturbance component of the voltage reference value is calculated using the following formula: ； in, and For small disturbance components of the voltage reference value, , , and These are the transfer functions of the PI regulator in the voltage and current control loops, respectively. , , , These are the reference values ​​for the amplitude of the VSG power outer loop output voltage. , The output currents in the dq coordinate system are respectively. This represents the small voltage disturbance component in the dq coordinate system at the grid connection point.

4. The VSG control method for oscillation instability according to claim 3, characterized in that, Calculate the positive sequence impedance using the following formula: ； in, It is a positive sequence impedance. It is the positive sequence voltage component. This is the positive sequence current component. For filtering inductors, For filtering capacitors, For filtering resistors, , for , The corresponding angular frequency, The transfer function for the current inner-loop PI controller. The transfer function for the voltage outer loop PI controller. , , , , All are characteristic polynomials. , These are the scaling factors for the current loop and the voltage loop, respectively. , These are the integral coefficients for the current loop and the voltage loop, respectively; Calculate the negative sequence impedance using the following formula: 。 5. The VSG control method for oscillation instability according to claim 1, characterized in that, Calculate the voltage and current tracking errors using the following formulas: ； in, For voltage tracking error, For current tracking error, , These are the expected values ​​of voltage and current, respectively. Let VSG be the steady-state component of the voltage value of the grid-connected system in the dq coordinate system. Let VSG be the steady-state component of the current value of the VSG in the grid-connected system in the dq coordinate system.

6. The 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, For sliding surface functions, The gain coefficient of the sliding surface. This is the current error signal. For time.

7. The VSG control method for oscillation instability according to claim 6, characterized in that, The current inner loop control rate is calculated using the following formula: ； ； in, For exponential convergence law, The rate of change of the d-axis reference current. This is the output voltage of the VSG. , , These are the filter inductor, inductor parasitic resistance, and filter capacitor of the inverter's LCL filter. The gain coefficient of the sliding surface. This is the current error signal. Output voltage of current inner loop integral sliding mode control.

8. The 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; Calculate the short-circuit ratio using the following formula: ； Where SCR is the short-circuit ratio. Rated power, This is the effective value of the rated phase voltage of the power grid. This is the equivalent impedance of the power grid.

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