VSG stability analysis method and system based on grid strength disturbance

Abstract

The application discloses a kind of VSG stability analysis method and system based on grid strength disturbance, belong to virtual synchronous generator control technical field;The method is by establishing the small signal model of VSG grid strength disturbance, the small signal model of grid strength change is introduced into the closed-loop control model of VSG system, deduces the coupling transfer function between grid strength disturbance and active power, reactive power;Further construct oscillation transfer function model, quantitatively analyze the influence of grid strength disturbance on system electrical quantity, and judge the stability of system under disturbance and oscillation transfer effect by transfer function amplitude;The application fills the blank that the influence of traditional small signal model is not considered grid strength change, can accurately predict the dynamic behavior of system under grid parameter perturbation, improve the precision and accuracy of stability analysis, provide theoretical basis and technical support for VSG system control parameter optimization and robustness improvement.

Description

Technical Field

[0001] This invention belongs to the field of virtual synchronous generator control technology, and relates to a method and system for VSG stability analysis based on grid strength disturbance. Background Technology

[0002] Grid-type virtual synchronous machines (VSGs) are a key technology for efficient grid connection of new energy sources, playing a significant role in improving the inertial support and damping performance of the power grid. However, in actual operation, grid strength (SCR) is often disturbed by factors such as line parameters and load changes, manifesting as changes in grid inductance and grid resistance, which in turn affect the output electrical quantities of the VSG system, causing low-frequency oscillations or even system instability.

[0003] Existing VSG stability analyses primarily focus on voltage stability, frequency stability, and power coupling effects. For example, Bode plots of open-loop transfer functions are used to analyze voltage and frequency stability, while state-space models and eigenvalue analysis are employed to study power oscillation mechanisms. However, traditional methods typically assume constant grid strength and fail to incorporate grid strength disturbances as independent variables into closed-loop models. This leads to difficulties in accurately assessing system stability and oscillation transmission mechanisms when grid parameters fluctuate, resulting in decreased accuracy in stability analysis. Furthermore, existing models fail to quantitatively reveal the dynamic coupling effects between grid strength disturbances and active and reactive power, and cannot predict the specific impact of disturbances on system output electrical quantities, thus limiting controller parameter optimization and system robustness improvement. Summary of the Invention

[0004] The technical solution of this invention aims to solve the problem that existing VSG stability analysis methods are usually based on the assumption of constant grid strength and do not fully consider the impact of grid parameter disturbances on system stability.

[0005] The present invention solves the above-mentioned technical problems through the following technical solutions:

[0006] This invention provides a method for VSG stability analysis based on power grid intensity disturbances, comprising the following steps: S1. Based on Kirchhoff's laws, derive the KVL and KCL equations of the VSG system. Combine the grid inductance disturbance and grid resistance disturbance for small-signal processing to obtain the small-signal equations of active power and reactive power of the VSG system. S2. Based on the coupling relationship between the active power, reactive power, grid inductive disturbance and grid resistive disturbance of the VSG system, establish the coupling influence relationship between the grid inductive disturbance and grid resistive disturbance on the active power and reactive power. S3. Considering the impact of grid intensity changes on the power oscillation stability of the VSG system, the oscillation propagation path of grid intensity disturbances to active power is obtained, thereby constructing the oscillation transfer function model of the VSG system under grid intensity disturbances; The VSG system takes a small-signal power reference value as input. By adding grid inductance and grid resistance disturbances, the expression for the VSG system output is: ,in, This represents the closed-loop transfer function of the active power of the VSG system. The transfer function represents the transmission from grid inductive disturbances to active power oscillations. This represents the transfer function that transmits grid resistance disturbances to active power oscillations. Power reference value, small signal quantity, grid inductance disturbance quantity ΔL g Power grid resistance disturbance ΔR g ; S4. Based on the amplitude of the oscillation transfer function at the system oscillation frequency, determine the stability and oscillation transfer effect of the system under disturbance conditions.

[0007] Furthermore, the small-signal equations for the active and reactive power of the VSG system are as follows:

[0008] in, The rated angular frequency, For active power small signal quantity, For reactive power small signal quantity, The inverter-side voltage is the d-axis steady-state component. This represents the q-axis steady-state component of the inverter-side voltage. This represents the d-axis steady-state component of the inverter-side current. This represents the q-axis steady-state component of the inverter-side current. This represents the small-signal component of the inverter-side output current along the d-axis. This represents the small-signal q-axis component of the inverter-side output current. The small-signal component of the output voltage along the d-axis of the VSG system. This refers to the small-signal q-axis output voltage of the VSG system. For the Labras operator.

[0009] Furthermore, the coupling relationship between the active power, reactive power, grid inductive disturbance, and grid resistive disturbance of the VSG system is as follows:

[0010] Among them, G LP (s) represents the coupling transfer function between grid inductive disturbance and active power, G RP(s) represents the coupling transfer function between grid resistance disturbance and active power. Let VSG active power output phase angle be the active power coupling transfer function. This is the voltage-active power coupling transfer function. The active power output phase angle and reactive power coupling transfer function of the VSG. This is the voltage-reactive power coupling transfer function. This is the transfer function for the coupling of grid inductive disturbance and reactive power. This is the transfer function for the coupling of grid resistance disturbance and reactive power. This is the phase angle disturbance. This represents the voltage amplitude disturbance. This represents the inductive disturbance of the power grid. This represents the disturbance in grid resistance.

[0011] Furthermore, the coupling effect of the grid inductive disturbance and the grid resistive disturbance on active power and reactive power is expressed as follows:

[0012] in, This indicates the coupling effect of grid impedance disturbances on active power. This indicates its coupling effect on reactive power.

[0013] Furthermore, the expression for the oscillation propagation path of the grid intensity disturbance to active power, thereby constructing the oscillation transfer function model of the VSG system under grid intensity disturbance, is as follows:

[0014] in, The transfer function represents the transmission from grid inductive disturbances to active power oscillations. G represents the transfer function that transmits grid resistance disturbances to active power oscillations. LP (s) represents the coupling transfer function between grid inductive disturbance and active power, G RP (s) represents the coupling transfer function between grid resistance disturbance and active power. Let VSG active power output phase angle be the active power coupling transfer function. This is the voltage-active power coupling transfer function. The active power output phase angle and reactive power coupling transfer function of the VSG. This is the voltage-reactive power coupling transfer function. This is the transfer function for the coupling of grid inductive disturbance and reactive power. Let D be the transfer function of the coupling between grid resistance disturbance and reactive power. pJ is the damping coefficient of the active power control system. p D is the inertia coefficient of the active power control element. q J is the damping coefficient of the reactive power control system. q The inertia coefficient of the reactive power control element.

[0015] The present invention also provides a VSG stability analysis system based on grid strength disturbances, comprising: Small-signal processing module: Based on Kirchhoff's laws, derive the KVL and KCL equations of the VSG system, combine grid inductive disturbance and grid resistive disturbance and perform small-signal processing to obtain the small-signal equations of active power and reactive power of the VSG system. Coupling relationship establishment module: Based on the coupling relationship between the active power, reactive power, grid inductive disturbance and grid resistive disturbance of the VSG system, establish the coupling influence relationship between grid inductive disturbance and grid resistive disturbance on active power and reactive power. Quantitative evaluation module: Considering the impact of grid intensity changes on the power oscillation stability of the VSG system, the oscillation propagation path of grid intensity disturbances to active power is obtained, thereby constructing the oscillation transfer function model of the VSG system under grid intensity disturbances; The VSG system takes a small-signal power reference value as input. By adding grid inductance and grid resistance disturbances, the expression for the VSG system output is: ,in, This represents the closed-loop transfer function of the active power of the VSG system. The transfer function represents the transmission from grid inductive disturbances to active power oscillations. This represents the transfer function that transmits grid resistance disturbances to active power oscillations. Power reference value, small signal quantity, grid inductance disturbance quantity ΔL g Power grid resistance disturbance ΔR g ; Judgment module: Based on the amplitude of the oscillation transfer function at the system oscillation frequency, determine the stability and oscillation transfer effect of the system under disturbance conditions.

[0016] Furthermore, the small-signal equations for the active and reactive power of the VSG system are as follows:

[0017] in, The rated angular frequency, For active power small signal quantity, For reactive power small signal quantity, The inverter-side voltage is the d-axis steady-state component. This represents the q-axis steady-state component of the inverter-side voltage. This represents the d-axis steady-state component of the inverter-side current. This represents the q-axis steady-state component of the inverter-side current. This represents the small-signal component of the inverter-side output current along the d-axis. This represents the small-signal q-axis component of the inverter-side output current. The small-signal component of the output voltage along the d-axis of the VSG system. This refers to the small-signal q-axis output voltage of the VSG system. For the Labras operator.

[0018] Furthermore, the coupling relationship between the active power, reactive power, grid inductive disturbance, and grid resistive disturbance of the VSG system is as follows:

[0019] in, This is the phase angle disturbance. This represents the voltage amplitude disturbance. This represents the inductive disturbance of the power grid. This represents the disturbance in grid resistance.

[0020] Furthermore, the coupling effect of the grid inductive disturbance and the grid resistive disturbance on active power and reactive power is expressed as follows:

[0021] in, This indicates the coupling effect of grid impedance disturbances on active power. This indicates its coupling effect on reactive power.

[0022] Furthermore, the expression for the oscillation propagation path of the grid intensity disturbance to active power, thereby constructing the oscillation transfer function model of the VSG system under grid intensity disturbance, is as follows:

[0023] in, The transfer function represents the transmission from grid inductive disturbances to active power oscillations. G represents the transfer function that transmits grid resistance disturbances to active power oscillations. LP (s) represents the coupling transfer function between grid inductive disturbance and active power, G RP (s) represents the coupling transfer function between grid resistance disturbance and active power. Let VSG active power output phase angle be the active power coupling transfer function. This is the voltage-active power coupling transfer function. The active power output phase angle and reactive power coupling transfer function of the VSG. This is the voltage-reactive power coupling transfer function. This is the transfer function for the coupling of grid inductive disturbance and reactive power. Let D be the transfer function of the coupling between grid resistance disturbance and reactive power. p J is the damping coefficient of the active power control system. p D is the inertia coefficient of the active power control element. q J is the damping coefficient of the reactive power control system. q The inertia coefficient of the reactive power control element.

[0024] The present invention also provides an electronic device, including a memory and a processor, wherein the memory is used to store a program that supports the processor in executing the above-described VSG stability analysis method based on grid strength disturbance, and the processor is configured to execute the program stored in the memory.

[0025] The present invention also provides a storage medium storing a computer program, which, when run by a processor, executes the steps of the above-described VSG stability analysis method based on power grid strength disturbance.

[0026] The beneficial effects of this invention are as follows: 1) This invention is based on the power, voltage, and current equations in the VSG system, and performs small-signal linearization on the equations to obtain the grid intensity disturbance variable ΔL. g With ΔR g The coupling effects with active and reactive power are respectively considered; the grid intensity disturbance variable ΔL is derived. g With ΔR g The other electrical quantities serve as the input and the transfer function as the output. The open-loop transfer function is used to quantitatively evaluate the impact of grid intensity disturbances on the response characteristics of the output electrical quantities of the VSG system. Through this oscillation transfer effect analysis framework, the intrinsic mechanism of low-frequency oscillations induced by grid-type converters under grid intensity disturbances can be revealed in depth, providing a theoretical basis for improving system stability and designing robust control strategies.

[0027] 2) Traditional VSG stability analysis typically uses closed-loop transfer functions, which are effective for stability analysis. However, when the VSG system is under grid intensity disturbance, the open-loop transfer function cannot accurately obtain the system's stability margin and cannot determine the system's stability performance. To address this issue, this invention introduces an oscillating transfer function for grid intensity disturbances and other electrical quantities. By calculating the amplitude of this oscillating transfer function at the oscillation frequency point and performing quantitative analysis of the amplitude, the output response state of each electrical quantity under disturbance conditions can be effectively determined. This invention can more accurately characterize the dynamic behavior of the system, thereby achieving accurate assessment of system stability under dynamic disturbances and improving stability.

[0028] 3) Traditional stability analysis models and methods typically neglect the oscillation transfer effect between electrical quantities, resulting in an inability to comprehensively assess system stability. This invention innovatively introduces an oscillation transfer effect function to quantitatively analyze the coupling effects between different electrical quantities. To overcome the aforementioned shortcomings of existing methods, this invention incorporates the oscillation transfer effect into system stability analysis, enabling more accurate identification of potential low-frequency oscillations or instability phenomena, thus providing a more comprehensive basis for system stability analysis.

[0029] 4) This invention further reveals the influence of oscillation transfer effect on the dynamic fluctuation amplitude of different electrical quantities and provides a method for quantitatively evaluating the oscillation transfer effect. It establishes a transfer function model of the transfer from grid intensity disturbance to active power. By obtaining the amplitude information of the oscillation transfer function model at the oscillation frequency point, the oscillation transfer characteristics and laws of the system can be predicted. This invention can accurately evaluate the range of dynamic fluctuations of various electrical quantities under grid intensity disturbance, which can be achieved through the grid intensity disturbance variable ΔL. g and ΔR g By calculating the oscillation amplitude of active power, the risk of low-frequency oscillations in active power is reduced, helping designers and engineers identify potential system stability problems and take timely control measures to prevent system instability. In summary, this invention reduces the risk of low-frequency oscillations in active power by calculating the grid intensity disturbance variable ΔL. g and ΔR g Small-signal linearization introduces an oscillation propagation model. Based on ΔL... g and ΔR g The oscillation transfer effect model transferred to active power can accurately predict the dynamic fluctuation amplitude of active power in VSG systems, significantly improving the accuracy and effectiveness of VSG system stability analysis and providing a more scientific and comprehensive method for power system stability assessment and optimization.

[0030] 5) This invention fills the gap in traditional small-signal models that do not consider changes in grid strength. Studies show that the relative error between the GSDM model and the switching model is close to zero, verifying the model's effectiveness. Eigenvalue analysis results show that the dominant oscillation mode obtained based on the oscillation propagation model of this invention basically coincides with the dominant oscillation mode of the traditional active power closed-loop model, further illustrating the model's universality and adaptability. This model provides a new perspective for predicting VSG active power oscillations and stability, and clearly elucidates the influence mechanism of grid strength changes on VSG stability and active power oscillations. Attached Figure Description

[0031] Figure 1 This is a block diagram illustrating the control principle of the VSG system. Figure 2This diagram illustrates the coupling relationship between active and reactive power in a VSG system. Figure 3 This is a diagram showing the coupling effect of grid inductive disturbance and grid resistive disturbance on active and reactive power. Figure 4 A comprehensive stability assessment framework diagram for the VSG system; Figures 5(a) to 5(i) are comparisons of the power grid intensity disturbance oscillation propagation model and the Simulink model under different conditions. Figure 6(a) shows the eigenvalue matching between the closed-loop control model and the open-loop model for power grid intensity disturbance, and Figure 6(b) shows the relative error between the closed-loop control model and the simulation. Figure 7(a) and Figure 7(b) show the step response results of active power under the IGSD (grid inductive disturbance) and RGSD (grid resistive disturbance) conditions, respectively. Figures 8(a) to 8(c) show the comparative simulation results of the GSDM (Grid Impedance Disturbance Transmission to Active Power Prediction Model of the Invention) model and the Simulink model under the same grid impedance disturbance and operating conditions, respectively, for the three enhanced auxiliary control strategies of Type 1–Type 3. Figures 9(a) to 9(c) show the grid inductance under the three enhanced auxiliary control strategies (Type 1–Type 3), respectively. Transfer function to active power The unit step response diagram; Figures 10(a) to 10(c) show the eigenvalue analysis results under the three enhanced control strategies Type 1–Type 3, respectively. Figure 11 Diagram of the HIL experimental platform; Figures 12(a) to 12(f) show the active power response results under different grid strength conditions (different short-circuit ratios SCR); Figures 13(a) to 13(c) show the experimental active power response results of the system under different auxiliary control strategies (Type1–Type3) when subjected to grid impedance disturbances. Detailed Implementation

[0032] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0033] The technical solution of the present invention will be further described below with reference to the accompanying drawings and specific embodiments: Example 1 This embodiment provides a method for modeling and stability analysis of VSG under power grid intensity disturbances, including: 1. Establish a small-signal model for power grid intensity disturbances. Based on Kirchhoff's laws, the KVL equations for the VSG system are as follows: (1) in, , , , , , , These represent the dq-axis components of the VSG system output current, respectively. , These represent the dq-axis components of the VSG system output voltage, respectively. , These are the dq-axis components of the grid voltage, respectively. , , The inductance value of the output filter of the VSG system. The parasitic resistance of the output filter of the VSG system. For grid-side inductance, Let be the grid-side resistance, and s be the Labras operator. From the perspective of the power grid, For the VSG system output angle, As the reference angular frequency, Output phase angle for VSG system. The output voltage amplitude of the VSG system. This is the reference voltage for the power grid.

[0034] Small-signal processing of the KVL equation yields: (2) in, The small-signal component of the output voltage along the d-axis of the VSG system. This refers to the small-signal q-axis output voltage of the VSG system. The steady-state value of the active power output phase angle of the VSG. This refers to the steady-state output voltage of the VSG system. This is the phase angle disturbance. This represents the voltage amplitude disturbance. This represents the inductive disturbance of the power grid. This represents the disturbance in grid resistance.

[0035] Based on Kirchhoff's laws, the KCL equations for the VSG system are as follows: (3) By performing small-signal processing on the KCL equations of the VSG system, the small-signal equations for the current of the VSG system are obtained as follows: (4) in, The transfer function matrix for coupling effects. This represents the small-signal component of the inverter-side output current along the d-axis. This represents the small-signal component of the q-axis output current on the inverter side.

[0036] Based on formulas (2) and (4), the small-signal equations for the active and reactive power of the VSG system are as follows: (6) in, The rated angular frequency, For active power small signal quantity, For reactive power small signal quantity, The inverter-side voltage is the d-axis steady-state component. This represents the q-axis steady-state component of the inverter-side voltage. This represents the d-axis steady-state component of the inverter-side current. This represents the steady-state q-axis component of the inverter-side current.

[0037] 2. Establish a closed-loop control model for power grid intensity disturbances. like Figure 2 As shown, considering the direct coupling between active and reactive power, the coupling relationships between active power, reactive power, grid inductive disturbance, and grid resistive disturbance in the VSG system are as follows: (7) Among them, G LP (s) represents the grid inductive disturbance ΔL g The coupling transfer function with active power, G RP (s) represents the grid resistance disturbance ΔR g The coupling transfer function with active power, Let VSG active power output phase angle be the active power coupling transfer function. This is the voltage-active power coupling transfer function. The active power output phase angle and reactive power coupling transfer function of the VSG. This is the voltage-reactive power coupling transfer function. This is the transfer function for the coupling of grid inductive disturbance and reactive power. This is the transfer function for the coupling of grid resistance disturbance and reactive power.

[0038] , , , , , , and The expressions are as follows:

[0039] Among them, R 11 (s), R 22 (s), Y 11 (s) and Y 22 (s) is an intermediate variable.

[0040] like Figure 3 As shown, the coupled effects of grid inductive disturbances and grid resistive disturbances on the dynamics of active and reactive power are expressed as follows: (8) in, This indicates the coupling effect of grid impedance disturbances on active power. This indicates its coupling effect on reactive power.

[0041] VSG systems typically use a small-signal input of the power reference value, further incorporating grid inductive and resistive disturbances. The output expression is as follows: (9) in, This represents the closed-loop transfer function of the VSG system. The transfer function represents the transmission from grid inductive disturbances to active power oscillations. It represents the transfer function that transmits grid resistance disturbances to active power oscillations.

[0042] The transfer function from grid inductive disturbance to active power oscillation The transfer function of power oscillations from grid resistance disturbances. The expression is as follows: (10) Substitute the operating parameters of the working condition into the transfer function G Lg-P (s) and G Rg-P (s) can be used to obtain the power grid intensity disturbance variable ΔL under the corresponding operating condition. g With ΔR g The relationship between the magnitude of the coupling effect and active power. Based on the grid intensity disturbance variable ΔL g With ΔRg The coupling effect with active power will affect the grid intensity disturbance variable ΔL. g With ΔR g and active power reference value disturbance ΔP ref Active power is used as the input variable and active power as the output variable. Each disturbance is analyzed separately, and the values ​​derived from the grid intensity disturbance variable ΔL are obtained. g With ΔR g and active power reference value disturbance ΔP ref The transfer function G transferred to active power Lg-P (s), G Rg-P (s) and G Pref-P (s). G Lg-P (s) and G Rg-P (s) is used to quantitatively analyze the impact of grid intensity disturbance variables ΔLg and ΔRg on the active power of the VSG system. Pref-P (s) is used for quantitative analysis of the active power reference value disturbance ΔP. ref The impact on the active power of the VSG system, the same G Pref-P (s) is the closed-loop transfer function of active power in the VSG system, which can be used to determine whether the system is stable.

[0043] 3. System stability assessment like Figure 4 As shown, this is the comprehensive stability assessment framework for the VSG system. The open-loop transfer function of the VSG system under grid intensity disturbances is constructed, and its Bode plot is plotted to assess system stability. System stability is quantitatively determined by analyzing the phase margin at the intersection of the amplitude-frequency response curve and 0 dB in the Bode plot. Specifically, the phase margin is defined as the phase of the amplitude response when it crosses 0 dB. The phase difference between 180° is considered; the larger this phase difference, the higher the system's stability margin, indicating stronger disturbance resistance and dynamic stability. Conversely, a smaller difference means a lower system stability margin, making it more susceptible to oscillations or instability caused by external disturbances or parameter fluctuations. This method provides a criterion for stability analysis and oscillation / instability risk assessment of VSG systems under different grid parameter disturbances, helping to guide controller design and parameter tuning.

[0044] according to Figure 1 From the control principle block diagram of the VSG system, the rotor motion equation of the VSG system can be obtained as follows: (11) Among them, D p J is the damping coefficient of the active power control system. p D is the inertia coefficient of the active power control element. q J is the damping coefficient of the reactive power control system. qThe inertia coefficient of the reactive power control system. This is a reference value for active power. This is a reference value for reactive power.

[0045] according to Figure 4 The open-loop transfer functions for active and reactive power can be derived as follows: (12) in, For the forward channel 1 transfer function, For the forward channel 2 transfer function, The characteristic determinant of the signal flow graph, For feedback channels, There are two non-adjacent feedback channels. There are 3 non-adjacent feedback channels. This refers to the portion where the feedback channel and the forward channel are not adjacent. For closed-loop transfer function This is the forward passage.

[0046] The open-loop transfer function described above is used to capture the critical oscillation frequency point of the active power of the VSG system under specific operating conditions.

[0047] By extracting the power grid intensity disturbance variable ΔL g With ΔR g The size of ΔL g With ΔR g With the power grid strength disturbance variable ΔL g With ΔR g The transfer function G transferred to active power Lg-P (s) and G Rg-P (s) are multiplied separately, and the power grid intensity disturbance variable ΔL is quantitatively calculated using Simulink. g With ΔR g Fluctuations in active power.

[0048] Based on the power grid intensity disturbance variable ΔL g With ΔR g Transmission to other electrical quantities, the oscillation transmission effect fully considers the grid strength disturbance variable ΔL. g With ΔR g Due to its coupling effect with active power, the oscillation transfer effect transfer function model can be used for analysis.

[0049] Based on the power grid intensity disturbance variable ΔL g With ΔR g The magnitude of the oscillation transfer effect between the active power and the active power can be quantitatively expressed as: (13) in, This indicates that the oscillation is caused by the grid strength disturbance ΔL g An oscillation transfer model for active power. The angular velocity at the oscillation frequency point, The inductive disturbance of the power grid ΔL g The magnitude of the oscillation transmission effect transferred to active power. If This indicates that the disturbance causes a positive feedback oscillation transmission effect, and as the corresponding As the value of increases, the positive feedback oscillation transmission effect becomes more pronounced, and the system stability decreases. Conversely, When this occurs, it indicates that the disturbance generates a negative feedback oscillation transmission effect, and as the corresponding As the value decreases, the negative feedback oscillation transmission effect becomes more pronounced, and the suppression effect becomes more significant, thus helping to reduce the risk of active power oscillations in virtual synchronous generator (VSG) systems. Similarly, This indicates that the oscillation is caused by the grid strength disturbance ΔR. g An oscillation transfer model for active power. For the power grid intensity disturbance ΔR g The magnitude of the oscillation transmission effect transferred to active power. If This indicates a positive feedback oscillation transmission effect, and as the corresponding As the value of increases, the positive feedback oscillation transmission effect becomes more pronounced, and the system stability decreases. Conversely, When this occurs, it indicates a negative feedback oscillation transmission effect, and as the corresponding... As the value decreases, the negative feedback oscillation transmission effect becomes more pronounced, and the suppression effect becomes more significant, thus helping to reduce the risk of active power oscillation in virtual synchronous generator (VSG) systems.

[0050] 4. Simulation verification To verify the model of this invention, a comparison was set up between the theoretical and simulation models, as shown in Figures 5(a) to 5(c), with control parameters... Under the condition that remains unchanged, respectively Comparative analyses were conducted using values ​​of 0.03, 0.06, and 0.1. It can be clearly observed that the active power time-domain responses obtained from the switching model and the GSDM model almost completely overlap, exhibiting highly consistent dynamic behavior. This fully demonstrates that the method of this invention has excellent accuracy in characterizing the dynamic characteristics of the system. With the increase of the virtual inertia level, the damping of power oscillations gradually weakens, while the oscillation frequency decreases accordingly, revealing the influence law of virtual inertia on the dynamic performance of the system. Furthermore, as shown in Figures 5(d) to 5(i), when the control parameters are fixed at... , Under the given conditions, the active power response under different grid impedance disturbances was compared and analyzed. The results show that the time-domain response of the switching model and the model of this invention remains highly consistent, further verifying the accuracy and reliability of the method of this invention. Meanwhile, as the grid impedance decreases, the damping performance of the power oscillation weakens, and the oscillation phenomenon becomes more pronounced, which further highlights the robustness and applicability of the GSDM model under different short-circuit ratios (SCR). It should be noted that... This indicates the active power offset.

[0051] To verify the accuracy of this invention, an oscillation propagation error analysis method based on power grid intensity disturbance is proposed, the expression of which is as follows: (14) in, and These represent the average active power values ​​obtained from the simulation model and the theoretical model at different times, respectively; and This indicates a situation in the simulation model where the active power fluctuation deviation is greater than or equal to 1% of the reference value; and These correspond to the number of times the active power fluctuation deviation is greater than or equal to 1% of the reference value. (Function) This represents the relative error ratio between the theoretical model and the simulation model.

[0052] To further verify the effectiveness of the grid impedance disturbance propagation to active power prediction model (GSDM) of this invention, a comparative analysis of eigenvalues ​​was conducted between GSDM and the active power closed-loop model (CLMAP model). As shown in Figure 6(a), the eigenvalues ​​of CLMAP are marked with "×", while the eigenvalues ​​of GSDM are marked with "○". It can be seen that the eigenvalues ​​of the two models are highly consistent, indicating a good matching degree between GSDM and CLMAP. This result proves that the GSDM model can effectively preserve the inherent dominant oscillation mode of the system without changing the basic dynamic characteristics of the system. Figure 6(b) shows the grid inductance after the disturbance. Under the condition of changing from 4mH to 11mH, the simulation model based on the switching model and the GSDM theoretical model ( , The power oscillation error between the simulation model and the theoretical model is shown to be within this range. and )right The dependence on [the specific component] is relatively weak, and the two remain highly consistent throughout; correspondingly, the relative error ratio (RER) is below 4% across the entire range. This is especially true for post-disturbance grid inductance. When it is in the range of 6mH to 8mH, The result is close to zero, indicating that the model has a very high degree of fit within this range, which has practical engineering significance. Outside this range, the error increases slightly, which may be due to the small-signal model's inability to fully reflect the residual switching harmonics and ripple effects, and the average value model's inability to simulate the inrush current generated during the switching process.

[0053] To further verify the accuracy of the GSDM model, this invention uses the oscillation transfer function and The Bode plot was compared with the experimental results. As shown on the right side of Figure 7(a), when the grid inductive disturbance... Power grid resistance disturbance At that time, transfer function The amplitude at the oscillation frequency gradually decreases as the grid strength decreases. This indicates that... The oscillatory effect of the disturbance being transferred to active power gradually weakens, resulting in a decrease in the oscillation amplitude of active power. Similarly, as shown on the left side of Figure 7(b), the transfer function... The amplitude at the oscillation frequency also decreases as the grid strength decreases. This means that... The oscillation transfer effect of disturbances to active power is weakened, thereby reducing the oscillation amplitude of active power. These results are in high agreement with experimental results, and the good consistency between theoretical analysis and experimental data further demonstrates the effectiveness and robustness of the GSDM model.

[0054] To further solidify the theoretical foundation of the GSDM model, this invention plots the unit step response of active power transmitted from disturbances in grid inductance and grid resistance to active power under traditional VSG control conditions. As shown on the right side of Figures 7(a) and 7(b), the step response results of active power are presented under IGSD and RGSD conditions, with parameters set to... , It can be observed that the active power response exhibits damped oscillation characteristics, and the steady-state error approaches zero. With the increase of grid inductance... As the inductance of the grid decreases, the oscillation amplitude increases and the damping process slows down. This phenomenon is consistent with the results of eigenvalue analysis, indicating that reducing the grid inductance... This weakens the system's damping performance, thereby reducing system stability. Furthermore, changes in grid strength disturbances do not affect the steady-state error of active power, a trend consistent with the Bode plot analysis results on the left side of Figures 7(a) and 7(b). To rigorously evaluate the robustness and accuracy of the GSDM model's modeling method, this invention introduces three auxiliary control strategies (referred to as Type 1, Type 2, and Type 3) and performs eigenvalue analysis and model matching verification on the model. Specifically, Type 1 represents a feedforward control loop from frequency to reactive power, used to characterize the direct impact of frequency changes on reactive power regulation. Type 2 represents a feedback control loop where active power and frequency are fed back to the control input, forming a closed-loop control mechanism that effectively enhances system damping and improves overall stability. Type 3 corresponds to a feedforward channel from frequency to active power, enabling the system to quickly adjust active power when frequency deviation occurs, thereby improving the system's inertial characteristics; this strategy compensates for the impact of voltage disturbances to a certain extent and helps maintain the accuracy of steady-state power. Based on the aforementioned enhanced auxiliary control scheme, this invention derives descriptions of grid inductance under three different auxiliary control types. and grid resistance The oscillatory transfer function of the disturbance being transferred to active power.

[0055] Under Type 1 control mode, the power grid intensity disturbance variable Δ L g and Δ R g The transfer function for transferring power to active power is:

[0056]

[0057] Under Type 2 control mode, the power grid intensity disturbance variable Δ L g and Δ R g The transfer function for transferring power to active power is:

[0058] Under Type 3 control mode, the power grid intensity disturbance variable ΔL g and ΔR g The transfer function for transferring power to active power is:

[0059]

[0060] Figures 8(a) to 8(c) show the comparative simulation results of the GSDM and Simulink models under the same grid impedance disturbances and operating conditions under three enhanced auxiliary control strategies. The simulation parameters are set as follows: , Meanwhile, the change in grid strength during the disturbance is characterized by varying the short-circuit ratio (SCR) from 4.9 to 6.3. The theoretical models corresponding to the three enhanced auxiliary control strategies are represented by the blue dashed lines in the figure; the red solid lines represent the output of the Simulink model. It can be clearly observed that the theoretical model results are highly consistent with the simulation model results under all three control types (Type 1–Type 3). This consistency indicates that GSDM can accurately characterize the dynamic response of active power and effectively predict its oscillation characteristics under different SCR conditions. Furthermore, the simulation results further demonstrate that even with the introduction of different enhanced auxiliary control strategies, the model maintains good robustness and reliability, thus verifying its applicability under a wide range of grid strength conditions.

[0061] Figures 9(a) to 9(c) show the grid inductance under three enhanced auxiliary control strategies. Transfer function to active power The unit step response. The response surface is plotted over time. In the plane, the vertical axis represents the active power deviation. With As the inductance increases, the oscillation amplitude gradually decreases and the decay rate increases significantly, indicating that a larger grid inductance can effectively improve the damping performance of the system, thereby enhancing the small-signal stability of the system.

[0062] Furthermore, the active power converged to its steady-state value under all operating conditions, indicating that all four control schemes, including the baseline control, can achieve zero steady-state error when facing changes in grid strength. The three enhanced auxiliary control strategies exhibit significant differences in damping characteristics. Type 1 and Type 2 controls have similar dynamic characteristics, exhibiting large overshoot, but... The oscillation decays relatively quickly within the range of variation. In contrast, Type 3 control further reduces the oscillation amplitude and shortens the system settling time, exhibiting superior robustness, especially under weak grid conditions.

[0063] Figure 10(a) shows the eigenvalue analysis results under the Type 1 assisted control strategy. In this analysis, the system parameters are set to... , In the figure, eigenvalues ​​of different colors correspond to different auxiliary control parameters, while eigenvalues ​​of the same color represent the same parameter configuration. It can be observed that as the grid strength decreases, the system's damping ratio gradually increases, while the oscillation frequency decreases accordingly. This indicates that, within the GSDM model framework, the weakening of grid strength, dominated by changes in grid inductance, can actually improve the system's damping performance to some extent. Furthermore, Figures 10(b) to 10(c) show the eigenvalue analysis results under Type 2 and Type 3 auxiliary control strategies, respectively. The system parameters in both cases are also set to... , To ensure consistency in the comparative analysis, it can be seen that the trend of characteristic value trajectory movement caused by changes in grid intensity is basically consistent under the three auxiliary control strategies, indicating that the dynamic characteristics of the system remain consistent under different auxiliary control strategies. The transfer function parameters corresponding to different enhanced auxiliary control schemes are summarized in Table 1.

[0064] Table 1. Transfer function parameters for different enhanced auxiliary control schemes (Type 1–Type 3)

[0065] 5. Experimental verification To further verify the accuracy and robustness of this invention, experimental verification was conducted on a hardware-in-the-loop (HIL) experimental platform. For example... Figure 11 As shown, the experimental system mainly consists of a HIL model, a controller, an I / O board, an oscilloscope, and a host computer for system configuration and data recording. The real-time simulator models the circuit with a simulation step size of 1 μs, thus accurately capturing the dynamic characteristics of the system. Simultaneously, the grid-type inverter controller operates at a sampling frequency of 10 kHz, ensuring that the control algorithm can be executed promptly and accurately during the HIL experiment.

[0066] Figures 12(a) to 12(f) show the active power response results under different grid strength conditions (characterized by different short-circuit ratios (SCRs)). In each operating condition, the purple curve represents the theoretical calculation result obtained from GSDM, while the yellow curve corresponds to the simulation result based on Simulink. It can be clearly seen that the two sets of waveforms almost completely overlap under all six operating conditions, fully demonstrating the high accuracy and high fidelity of the GSDM model.

[0067] Furthermore, under all grid intensity disturbance conditions, the active power response exhibits good damping characteristics and superior dynamic performance. The high consistency between theoretical and simulation results demonstrates that the GSDM can accurately characterize the transient and steady-state behavior of active power. These results further validate the effectiveness, robustness, and engineering application value of the model under a wide range of grid intensity variation scenarios.

[0068] Figures 13(a) to 13(c) show the experimental active power response results of the system under different auxiliary control strategies when subjected to grid impedance disturbances. The experimental parameters were set as follows: , Grid strength was characterized by the short-circuit ratio (SCR), ranging from 4.9 to 6.3. Under all experimental conditions, active power returned to its steady-state value after the disturbance occurred without significant steady-state deviation, verifying the steady-state accuracy of the GSDM-based model. Furthermore, the transient response observed in the experiment was highly consistent with the Simulink simulation results, further validating the fidelity and reliability of the theoretical model. Further analysis showed that the auxiliary control strategy could significantly reduce the oscillation component generated by grid impedance disturbances. All three auxiliary control strategies achieved faster oscillation decay rates and smaller oscillation amplitudes, with Type 3 showing the most significant improvement. These results demonstrate that combining GSDM with appropriate auxiliary control strategies can effectively improve the transient stability and robustness of the system under different grid strength conditions.

[0069] This invention addresses the power grid intensity disturbance variable ΔL. g With ΔR g Small-signal linearization is applied and then introduced into the power control loop. Further analysis is performed on the grid intensity disturbance variable ΔL. g With ΔR g The amplitude characteristics of the oscillation transfer function of the active power transferred to the VSG at the oscillation frequency point can be used to determine the grid intensity disturbance variable ΔL. g With ΔR gThis method addresses the impact of grid intensity disturbances on the active power output of a VSG. Based on an oscillation transfer effect model, it quantitatively assesses the impact of grid intensity disturbances on output electrical quantity fluctuations by extracting the magnitude of the disturbance and multiplying it by the disturbance oscillation transfer function. This reveals the mechanism by which grid intensity disturbances affect the low-frequency oscillations of the VSG system, providing a novel approach to reducing the impact of disturbance transfer effects. Unlike traditional VSG models, existing methods do not incorporate grid intensity disturbances into closed-loop considerations in stability analysis, making it difficult to accurately assess their impact on system output electrical quantities when grid intensity disturbances occur. Furthermore, the closed-loop transfer function of traditional VSG systems primarily focuses on the coupling relationship between active and reactive power, failing to comprehensively consider the coupling effect between grid intensity disturbances and active and reactive power. Consequently, it cannot quantify the impact of grid intensity disturbances of different magnitudes on system stability in stability analysis. This invention can accurately assess the stability of a VSG system under grid intensity disturbance conditions. The proposed discrimination criterion possesses good adaptability and universality, providing a solid theoretical basis for the parameter design of virtual synchronous machine controllers. The research results show that, compared with traditional self-closed-loop control strategies, the stability analysis method and discrimination criteria of this invention significantly improve the accuracy and robustness of system stability assessment when dealing with grid intensity disturbances. Experimental results show that the method has good adaptability and practicality in new energy power generation systems, and can effectively improve the accuracy of system stability analysis under grid parameter fluctuation conditions. In addition, the eigenvalue distribution of the grid intensity disturbance oscillation transfer function of this invention matches well with the active power closed-loop eigenvalue distribution. More importantly, to further verify the applicability of the method, this invention introduces an auxiliary enhanced control strategy, thus verifying the adaptability of the method. All examples show that the GSDM model modeling method has universality, and the modeling method is verified by hardware-in-the-loop (HIL) experiments. This provides a theoretical basis and engineering guidance for the parameter design of grid-type virtual synchronous machine controllers and the improvement of system robustness. Addressing the problem of overly simplistic solutions in existing technologies, this invention proposes a significantly different solution, mainly providing a comprehensive analysis method for the stability assessment and oscillation transfer effect of grid-type converter systems under grid intensity disturbances. This method can comprehensively consider the overall stability of the system, evaluate the output response characteristics of the system from multiple dimensions, and reveal the dynamic response laws of grid intensity disturbances and other electrical quantities in the VSG system, providing a scientific basis for the optimization of system control strategies and parameter tuning.

[0070] Example 2 This embodiment provides a VSG stability analysis system based on power grid strength disturbance, including: a small signal processing module, a coupling relationship establishment module, a quantitative evaluation module, and a judgment module; The small-signal processing module derives the KVL and KCL equations of the VSG system based on Kirchhoff's laws, combines grid inductive disturbances and grid resistive disturbances with small-signal processing, and obtains the small-signal equations for the active and reactive power of the VSG system.

[0071] The small-signal equations for the active and reactive power of the VSG system are as follows:

[0072] in, The rated angular frequency, For active power small signal quantity, For reactive power small signal quantity, The inverter-side voltage is the d-axis steady-state component. This represents the q-axis steady-state component of the inverter-side voltage. This represents the d-axis steady-state component of the inverter-side current. This represents the steady-state q-axis component of the inverter-side current.

[0073] The coupling relationship establishment module establishes the coupling influence relationship between the grid inductive disturbance and the grid resistance disturbance on the active power and reactive power based on the coupling relationship between the active power, reactive power, grid inductive disturbance and grid resistance disturbance of the VSG system. The coupling relationships between the active power, reactive power, grid inductive disturbance, and grid resistive disturbance of the VSG system are as follows:

[0074] Among them, G LP (s) represents the coupling transfer function between grid inductive disturbance and active power, G RP (s) represents the coupling transfer function between grid resistance disturbance and active power. Let VSG active power output phase angle be the active power coupling transfer function. This is the voltage-active power coupling transfer function. The active power output phase angle and reactive power coupling transfer function of the VSG. This is the voltage-reactive power coupling transfer function. This is the transfer function for the coupling of grid inductive disturbance and reactive power. This is the transfer function for the coupling of grid resistance disturbance and reactive power.

[0075] The coupling effect of the grid inductive disturbance and the grid resistive disturbance on active power and reactive power is expressed as follows:

[0076] in, This indicates the coupling effect of grid impedance disturbances on active power. This indicates its coupling effect on reactive power.

[0077] The quantitative assessment module considers the impact of grid strength changes on the power oscillation stability of the VSG system, obtains the oscillation propagation path from grid strength disturbance to active power, and thus constructs an oscillation transfer function model of the VSG system under grid strength disturbance, which is used to quantitatively assess the impact of grid strength disturbance on active power. The expression for the oscillation propagation path of the grid intensity disturbance transmitted to active power is:

[0078] The VSG system takes a small-signal power reference value as input, and by adding grid inductance and grid resistance disturbances, its output is expressed as:

[0079] in, This represents the closed-loop transfer function of the VSG system. The transfer function represents the transmission of inductive disturbances in the power grid to active power oscillations. It represents the transfer function that transmits grid resistance disturbances to active power oscillations.

[0080] The judgment module determines the stability and oscillation transfer effect of the system under disturbance conditions based on the amplitude of the oscillation transfer function at the system oscillation frequency point.

[0081] Example 3 An electronic device includes a memory and a processor, the memory being used to store a program that supports the processor in executing the VSG stability analysis method based on grid strength disturbances as described in Embodiment 1, the processor being configured to execute the program stored in the memory.

[0082] Example 4 A storage medium storing a computer program, which, when executed by a processor, performs the steps of the VSG stability analysis method based on grid strength disturbances in Embodiment 1.

[0083] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for VSG stability analysis based on power grid intensity disturbances, characterized in that, Includes the following steps: S1. Based on Kirchhoff's laws, derive the KVL and KCL equations of the VSG system. Combine the grid inductance disturbance and grid resistance disturbance for small-signal processing to obtain the small-signal equations of active power and reactive power of the VSG system. S2. Based on the coupling relationship between the active power, reactive power, grid inductive disturbance and grid resistive disturbance of the VSG system, establish the coupling influence relationship between the grid inductive disturbance and grid resistive disturbance on the active power and reactive power. The coupling effect of the grid inductive disturbance and the grid resistive disturbance on active power and reactive power is expressed as follows: in, This indicates the coupling effect of grid impedance disturbances on active power. This indicates its coupling effect on reactive power, G LP (s) represents the coupling transfer function between grid inductive disturbance and active power, G RP (s) represents the coupling transfer function between grid resistance disturbance and active power. This is the transfer function for the coupling of grid inductive disturbance and reactive power. Let be the transfer function of the coupling between grid resistance disturbance and reactive power, and ΔL be the grid inductive disturbance. g Power grid resistance disturbance ΔR g ; S3. Considering the impact of grid intensity changes on the power oscillation stability of the VSG system, the oscillation propagation path of grid intensity disturbances to active power is obtained, thereby constructing the oscillation transfer function model of the VSG system under grid intensity disturbances, as shown in the following expression: in, The transfer function represents the transmission from grid inductive disturbances to active power oscillations. This represents the transfer function that transmits grid resistance disturbances to active power oscillations. Let VSG active power output phase angle be the active power coupling transfer function. This is the voltage-active power coupling transfer function. The active power output phase angle and reactive power coupling transfer function of the VSG. Let D be the voltage-reactive power coupling transfer function. p J is the damping coefficient of the active power control system. p D is the inertia coefficient of the active power control element. q J is the damping coefficient of the reactive power control system. q The inertia coefficient of the reactive power control system. This is the rated angular frequency; The VSG system takes a small-signal power reference value as input. By adding grid inductance and grid resistance disturbances, the expression for the VSG system output is: ,in, For active power small signal quantity, This represents the closed-loop transfer function of the active power of the VSG system. This represents a small-signal quantity indicating a power reference value. S4. Based on the amplitude of the oscillation transfer function at the system oscillation frequency, determine the stability and oscillation transfer effect of the system under disturbance conditions.

2. The VSG stability analysis method based on grid strength disturbance as described in claim 1, characterized in that, The small-signal equations for the active and reactive power of the VSG system are as follows: in, For reactive power small signal quantity, The inverter-side voltage is the d-axis steady-state component. This represents the q-axis steady-state component of the inverter-side voltage. This represents the d-axis steady-state component of the inverter-side current. This represents the q-axis steady-state component of the inverter-side current. This represents the small-signal component of the inverter-side output current along the d-axis. This represents the small-signal q-axis component of the inverter-side output current. The small-signal component of the output voltage along the d-axis of the VSG system. This refers to the small-signal q-axis output voltage of the VSG system. For the Labras operator.

3. The VSG stability analysis method based on grid strength disturbance as described in claim 2, characterized in that, The coupling relationship between the active power, reactive power, grid inductive disturbance, and grid resistive disturbance of the VSG system is as follows: in, This is the phase angle disturbance. This represents the voltage amplitude disturbance.

4. A VSG stability analysis system based on power grid intensity disturbances, characterized in that, include: Small-signal processing module: Based on Kirchhoff's laws, derive the KVL and KCL equations of the VSG system, combine grid inductive disturbance and grid resistive disturbance and perform small-signal processing to obtain the small-signal equations of active power and reactive power of the VSG system. Coupling relationship establishment module: Based on the coupling relationship between the active power, reactive power, grid inductive disturbance and grid resistive disturbance of the VSG system, establish the coupling influence relationship between grid inductive disturbance and grid resistive disturbance on active power and reactive power. The coupling effect of the grid inductive disturbance and the grid resistive disturbance on active power and reactive power is expressed as follows: in, This indicates the coupling effect of grid impedance disturbances on active power. This indicates its coupling effect on reactive power, G LP (s) represents the coupling transfer function between grid inductive disturbance and active power, G RP (s) represents the coupling transfer function between grid resistance disturbance and active power. This is the transfer function for the coupling of grid inductive disturbance and reactive power. Let be the transfer function of the coupling between grid resistance disturbance and reactive power, and ΔL be the grid inductive disturbance. g Power grid resistance disturbance ΔR g ; Quantitative evaluation module: Considering the impact of grid intensity changes on the power oscillation stability of the VSG system, the oscillation propagation path of grid intensity disturbances to active power is obtained, thereby constructing the oscillation transfer function model of the VSG system under grid intensity disturbances, as shown in the following expression: in, The transfer function represents the transmission from grid inductive disturbances to active power oscillations. This represents the transfer function that transmits grid resistance disturbances to active power oscillations. Let VSG active power output phase angle be the active power coupling transfer function. This is the voltage-active power coupling transfer function. The active power output phase angle and reactive power coupling transfer function of the VSG. Let D be the voltage-reactive power coupling transfer function. p J is the damping coefficient of the active power control system. p D is the inertia coefficient of the active power control element. q J is the damping coefficient of the reactive power control system. q The inertia coefficient of the reactive power control system. The rated angular frequency; The VSG system takes a small-signal power reference value as input. By adding grid inductance and grid resistance disturbances, the expression for the VSG system output is: ,in, For active power small signal quantity, This represents the closed-loop transfer function of the active power of the VSG system. This represents a small-signal quantity indicating a power reference value. Judgment module: Based on the amplitude of the oscillation transfer function at the system oscillation frequency, determine the stability and oscillation transfer effect of the system under disturbance conditions.

5. The VSG stability analysis system based on grid strength disturbance as described in claim 4, characterized in that, The small-signal equations for the active and reactive power of the VSG system are as follows: in, For reactive power small signal quantity, The inverter-side voltage is the d-axis steady-state component. This represents the q-axis steady-state component of the inverter-side voltage. This represents the d-axis steady-state component of the inverter-side current. This represents the q-axis steady-state component of the inverter-side current. This represents the small-signal component of the inverter-side output current along the d-axis. This represents the small-signal q-axis component of the inverter-side output current. The small-signal component of the output voltage along the d-axis of the VSG system. This refers to the small-signal q-axis output voltage of the VSG system. For the Labras operator.

6. The VSG stability analysis system based on grid strength disturbance as described in claim 5, characterized in that, The coupling relationships between the active power, reactive power, grid inductive disturbance, and grid resistive disturbance of the VSG system are as follows: in, This is the phase angle disturbance. This represents the voltage amplitude disturbance.

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