Method for suppressing low-frequency oscillation of grid-forming inverter based on damping torque
By introducing an additional damping branch into the power control loop of the grid-connected inverter and optimizing the system damping ratio using a damping torque model, the low-frequency oscillation problem of the VSG was solved, and the system stability was improved.
Patent Information
- Application Number
- CN202511659890.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-13
- Publication Date
- 2026-02-24
AI Technical Summary
Grid-type inverters suffer from low-frequency oscillations in terms of small-signal stability. Existing technologies struggle to effectively increase system damping without affecting droop characteristics, and additional damping control branches are difficult to implement in practical control systems.
By establishing a small-signal model of a virtual synchronizer, a damping torque model is derived, and an additional damping branch is introduced into the power control loop. A high-pass filter function is used to convert the synchronous torque into damping torque, thereby enhancing the system's damping torque to suppress low-frequency oscillations.
Without altering the steady-state operation of the system, the equivalent positive damping torque of the VSG was increased, the system damping ratio was optimized, low-frequency oscillations were effectively suppressed, and the system stability was improved.
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Figure CN121566503A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of stability control technology for grid-connected inverters, specifically a method for suppressing low-frequency oscillations in grid-connected inverters based on damping torque. Background Technology
[0002] With the country proposing the development goals of carbon peaking and carbon neutrality, building a new power system with new energy as the mainstay and promoting green, low-carbon and sustainable circular economic development have become urgent needs to address energy and environmental challenges.
[0003] Grid-connected inverters, represented by Virtual Synchronous Generator (VSG) control, possess excellent grid support capabilities and stability, and will play a greater role in the future integration of large-scale renewable energy into the grid. Although VSG simulates the dynamic behavior of a Synchronous Generator (SG), it inevitably inherits some characteristics of SG. Regarding small-signal stability, VSG inherits the low-frequency oscillation problem of SG, and due to insufficient equivalent damping ratio, it affects the inverter's operational stability and performance.
[0004] To suppress low-frequency oscillations in a VSG, it is typically necessary to increase the system's damping without affecting the droop characteristics. Current research focuses on adaptive damping control or adding additional damping control branches to control methods to achieve this. Adaptive damping control methods primarily optimize the system's damping ratio by dynamically adjusting control parameters in real time. Based on certain constraints, they calculate and apply control parameters that ensure the system operates at the optimal damping ratio. However, most studies using this method require obtaining the change in angular frequency, but it is rare to accurately obtain this change during dynamic processes, and it also places high demands on the controller.
[0005] The method of adding an auxiliary damping control branch mainly improves the equivalent damping ratio by adding an auxiliary branch between the active and reactive power loops of the VSG. Existing research adds feedback or feedforward control branches between the active and reactive power loops, but it is important to note that pure differential terms should be avoided in practical designs, as they are often difficult to implement in actual control systems. Furthermore, if division operations are involved in the additional control branch, it is necessary to ensure that the denominator in the actual control system does not approach zero to avoid the risk of system collapse during transient processes. Summary of the Invention
[0006] The purpose of this invention is to overcome the shortcomings of the prior art and propose a low-frequency oscillation suppression method for grid-type inverters based on damping torque. This method combines the damping torque method with a small-signal model and introduces an additional damping branch in the power control loop. This provides additional damping without affecting the operation of the original system, thereby improving the low-frequency oscillation phenomenon of the VSG.
[0007] To achieve the above objectives, the technical solution specifically adopted by the present invention is as follows:
[0008] A method for suppressing low-frequency oscillations in a grid-type inverter based on damping torque includes the following steps:
[0009] S1. Establish a small-signal model of the virtual synchronizer;
[0010] S101. Select state variables based on the grid connection circuit diagram of the virtual synchronous machine and construct a nonlinear system expression;
[0011] S102. Introduce a small disturbance at the steady-state equilibrium point and linearize to obtain a linear system in state-space form;
[0012] S103. Determine the system's output matrix to form a complete small-signal model;
[0013] S2. Based on the small-signal model, derive the damping torque model;
[0014] S201. Transform the small-signal model into an equivalent active power control loop block diagram;
[0015] S202. Identify and separate the synchronous torque and damping torque based on the equivalent active power control loop block diagram.
[0016] S203. Based on synchronous torque and damping torque, establish a damping torque model and analyze its impact on the dynamic characteristics of the system.
[0017] S3. Introduce an additional damping branch in the power control loop to enhance the damping torque of the system;
[0018] S4. The effect of the additional damping branch on suppressing low-frequency oscillations is verified by simulation.
[0019] Preferably, in step S101, the selected state variable is x. i =[δ,ω vsg E vsg ] T , where δ=θ o -θ g For U o V g The difference in their vector angles, θ o θ g It is the angle between the two; ωvsg It is the angular frequency of the virtual synchronizer; E vsg This serves as a reference for the output voltage amplitude.
[0020] Preferably, in S101, the expression for the nonlinear system is:
[0021]
[0022] Define a stable equilibrium point x i0 =[δ0,ω0,E0] T And at the stable equilibrium point x i0 =[δ0,ω0,E0] T Add a small perturbation Δx at the location i0 =[Δδ,Δω vsg ,ΔE vsg ] T Where ω0 is the equilibrium point angular frequency, E0 is the equilibrium point voltage amplitude, and P ref It is the active power reference value, P out The actual value of active power, Q ref This is the reactive power reference value, Q. out This is the actual value of reactive power, D. f The active circuit damping coefficient, D q J is the reactive power loop droop factor, and K is the active power loop inertia factor. q This is the reactive power loop inertia coefficient. Thus, the linear system is obtained:
[0023]
[0024] Based on the state matrix A0 and the input matrix B0, let Δy = [Δδ, Δω]. vsg ,ΔE vsg ,ΔP out ,ΔQ out ] T Let Δ represent the small-signal change, and let C0 be the output of the system. This yields the final small-signal model, expressed as follows:
[0025]
[0026] Preferably, the expression for the synchronous torque is as follows: T E =P m sin(δ1). Where P m δ1 is the electromagnetic power, and δ1 is the generator power angle.
[0027] The damping torque is expressed as follows: Where B is the damping coefficient. It is the rate of change of the work angle.
[0028] Preferably, the damping torque model expression is as follows:
[0029] Equivalent positive synchronous torque:
[0030] Where T E It is synchronous torque, w n It is the rated angular frequency, and the loop equivalent gain G. E .
[0031] Equivalent positive damping torque:
[0032] Where T D It is the damping torque.
[0033] Preferably, step S3 includes the following sub-steps:
[0034] S301. Add a high-pass filter function to the synchronous torque feedback branch to convert the synchronous torque into damping torque;
[0035] S302. Through equivalent transformation, the additional branch is simplified into a transfer function containing additional coefficients and time constant;
[0036] S303. The simplified feedback branch is introduced into the active power loop to form an additional damping control structure.
[0037] Preferably, the expression for the high-pass filter function is as follows:
[0038] Where K is the gain coefficient, w c It is the cutoff angular frequency.
[0039] Preferably, the expression for the transfer function is as follows:
[0040]
[0041] Preferably, the additional damping control structure formed in S303 is as follows:
[0042]
[0043] Where F(s) is the transfer function of the additional torque branch, and K1 and K are gain coefficients.
[0044] Preferably, the additional damping branch feeds back the state variables of the reactive power loop to the active power loop, simulating the dynamic characteristics of the excitation regulator to enhance system damping.
[0045] Preferably, step S4 includes the following sub-steps:
[0046] S401. Construct a virtual synchronous machine grid-connected simulation model;
[0047] S402. Apply a power step disturbance on the steady-state basis;
[0048] S403. Compare the system response with and without additional damping branches to verify the oscillation suppression effect.
[0049] This invention has the following characteristics and beneficial effects:
[0050] Without altering the steady-state operation of the system, the equivalent positive damping torque of the VSG was increased. An additional branch was introduced into the power control loop to rationally control system parameters, thereby optimizing the system's damping ratio, suppressing low-frequency oscillations, and improving the system's damping ratio, thus enhancing system stability. Attached Figure Description
[0051] Figure 1 This is a schematic diagram of the VSG small-signal model in an embodiment of the present invention.
[0052] Figure 2 for Figure 1 The equivalent APCL block diagram.
[0053] Figure 3 This is a closed-loop transfer block diagram of the VSG damped torque model.
[0054] Figure 4 This is a vector diagram of the VSG damping torque.
[0055] Figure 5 for Figure 3 Equivalent diagram with additional feedback branches.
[0056] Figure 6 for Figure 5 A schematic diagram of the separated torque components.
[0057] Figure 7 for Figure 6 G in the middle replacement E The equivalent block diagram after that.
[0058] Figure 8 for Figure 7 China G F Transform into G F1 The equivalent block diagram.
[0059] Figure 9 for Figure 8 China G F1 Transform into G F2 The equivalent block diagram.
[0060] Figure 10 This is the final control block diagram of an embodiment of the present invention.
[0061] Figure 11 This is a conventional VSG grid connection block diagram and main circuit.
[0062] Figure 12 P with or without inhibition strategy out Comparison diagram.
[0063] Figure 13 E with or without suppression strategy vsg Comparison diagram.
[0064] Figure 14 This is a schematic diagram comparing w with and without the suppression strategy.
[0065] Figure 15 Q is the expression with or without a suppression strategy. out Comparison diagram. Detailed Implementation
[0066] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.
[0067] A method for suppressing low-frequency oscillations in a grid-type inverter based on damping torque includes the following steps:
[0068] Step 1: Establish the VSG (Virtual Synchronizer) small-signal model.
[0069] This embodiment uses the VSG grid connection block diagram and main circuit as the basic circuit, such as Figure 11 As shown, where L f and C f U represents the filter inductor and filter capacitor, respectively. i and I f R represents the voltage and current vectors on the inverter side. g and X g P represents the equivalent resistance and equivalent inductance. out and Q out This corresponds to the active and reactive power injected into the power grid after passing through the point of common coupling (PCC).
[0070] The purpose of the power control loop is to generate a voltage reference at the point of common coupling, while the active power loop generates a phase angle signal to ensure synchronization with the power grid. See equations (1) and (2):
[0071]
[0072] θ vsg =∫ω vsg (2)
[0073] Where P ref For active power reference, J is the inertia coefficient, and D... f θ is the damping coefficient. vsg This serves as the phase reference for the output.
[0074] The reactive power loop is used to generate a voltage amplitude reference, as shown in equation (3):
[0075]
[0076] Q ref For reactive power reference, K q D is the coefficient of inertia. q E is the reactive power droop factor. ref E is the rated voltage amplitude. vsg This serves as a reference for the output voltage amplitude.
[0077] In this embodiment, average power modeling is used. The average power is obtained by passing the collected instantaneous power through a first-order low-pass filter. The average active power P can be obtained according to the line power flow relationship. out and average reactive power Q out :
[0078]
[0079] in For U o Amplitude, δ = θ o -θ g For U o V g The difference in their vector angles. Z T =R T +jX T =R g +jX g This represents the impedance between the VSG and the power grid.
[0080] In practical applications, considering the influence of factors such as transmission lines and transformer leakage inductance, the reactance component is usually significantly larger than the resistance component, i.e., X T ≥R T This characteristic is particularly pronounced in medium- and high-voltage power grids and long-distance transmission lines. Additionally, the voltage signal E generated by the power loop... vsg ∠θ vsg That is, the filter capacitor C. f The terminal voltage signal, therefore P out and Q out It can be simplified to:
[0081]
[0082] δ=θ vsg -θg =ω vsg t-ω g t (8)
[0083] First, select three state variables x of VSG. i =[δ,ω vsg E vsg ] T , where δ=θ o -θ g For U o V g The difference in their vector angles, θ o θ g It is the angle between the two; ω vsg It is the angular frequency of the virtual synchronizer; E vsg This serves as a reference for the output voltage amplitude.
[0084] Combining equations (1), (3), (6), and (8), write the expression for the nonlinear system:
[0085]
[0086] At the stable equilibrium point x i0 =[δ0,ω0,E0] T Add a small perturbation Δx at the location i0 =[Δδ,Δω vsg ,ΔE vsg ] T Combining equations (1) and (3), the system input quantity is set to Δu = [ΔP]. ref ,ΔQ ref ] T , for P out and Q out In x i0 Linearization yields:
[0087]
[0088] Transform equation (9) into the state-space form of a linear system:
[0089]
[0090] Where the state matrix A0 and the input matrix B0 are respectively:
[0091]
[0092] Let Δy = [Δδ, Δω] vsg ,ΔE vsg ,ΔP out ,ΔQ out ] T Given the system's output, we obtain the system's output matrix C0:
[0093]
[0094] Combining equations (12), (13), and (14), we finally obtain the complete linear system, such as... Figure 1 As shown, its mathematical expression is as follows:
[0095]
[0096] in:
[0097]
[0098] Where E0 is the voltage amplitude of the virtual synchronous machine, X T It is the total inductive reactance of the line, V gv It is the voltage amplitude of the power grid.
[0099] Step 2: Based on the small-signal model, derive the damping torque model.
[0100] The small-signal model of VSG, after equivalent transformation, can be obtained as follows: Figure 2 The equivalent APCL block diagram is shown below.
[0101] The synchronous torque and damping torque are identified and separated based on the equivalent active power control loop diagram.
[0102] The expression for synchronous torque is as follows:
[0103] T E =P m sin(δ1)
[0104] Among them, P m It is electromagnetic power, and δ1 is the generator power angle;
[0105] The damping torque is expressed as follows:
[0106]
[0107] Where B is the damping coefficient. It is the rate of change of the work angle.
[0108] This yields the closed-loop feedback parameter ΔP. out The expression:
[0109]
[0110] Where ΔT E This represents the equivalent torque acting on the VSG through the equivalent APCL. The expression for the equivalent positive synchronous torque is:
[0111]
[0112] Where the loop gain G E Influenced by the steady-state operating point and considering the system parameters, it is always a normal value, meaning ΔT E Always with Δδ vsg Since they are in the same direction, they can be considered as positive equivalent synchronous torques.
[0113] According to the equivalent APCL block diagram, the equivalent positive damping torque can be obtained as follows:
[0114]
[0115] From G D From the expression of ΔT D Advance Δδ vsg (s)90°, therefore the damping coefficient D P Determined ΔT D It provides a positive damping torque to the system. Moreover, in most cases, the positive synchronizing torque is much greater than the positive damping torque.
[0116] The damping torque model of the VSG system can be established from equations (17) and (18), such as Figure 3 As shown.
[0117] like Figure 4 As shown, a damping torque model for the VSG is established, where the damping torque T... D and synchronous torque T E Both factors influence the dynamic characteristics of the virtual synchronizer; the resultant torque of both is defined as T. Σ When a virtual synchronizing mechanism provides positive damping torque and synchronizing torque, the system remains stable. A larger damping torque provides a greater damping ratio, thus mitigating low-frequency oscillations. Synchronizing torque improves the system's synchronization characteristics; positive synchronizing torque enables the system to regain synchronization after disturbances. Otherwise, the system will diverge.
[0118] Step 3: Introduce an additional damping branch in the power control loop to enhance the system's damping torque.
[0119] Specifically, based on the aforementioned analysis, T E Always with θ vsg The equivalent positive synchronous torque is in phase and has a large amplitude. Therefore, if the large positive synchronous torque can be rotated, a positive damping torque component with the same direction as the equivalent damping torque can be obtained, thereby continuously providing positive damping torque and effectively enhancing the low-frequency oscillation suppression effect of the system.
[0120] To achieve the above objectives, a rotation term is added to the feedback branch of the original equivalent positive synchronous torque to ensure that the rotated torque component significantly increases the damping torque component. As shown in the figure below, adding a high-pass filter function to the positive synchronous torque branch advances the larger synchronous torque by a certain angle, thereby increasing the damping torque component and improving the system's ability to suppress low-frequency oscillations. K is the additional coefficient.
[0121] Then, by performing an equivalent transformation on the above block diagram, an additional feedback branch can be added to the original two synchronous torque and damping torque feedback branches. After decomposition, this additional feedback branch can increase the damping torque of the system, thereby suppressing the low-frequency oscillation effect of the system.
[0122] like Figure 5 , 6 As shown, the additional feedback branch is T. F ,and The next step is to perform equivalent transformations to find the most reasonable and effective control structure to construct the transfer function for low-frequency oscillation suppression.
[0123] G E All internal functions integrate the previously constructed VSG small-signal model. Therefore, G can be used... E The above block diagram can be broken down as shown.
[0124] According to the equivalent APCL block diagram And because of T F =G F *θ pcc
[0125] like Figure 7 As shown, feedback branch T F It can be simplified to Figure 8 G in F1
[0126] in As shown in the above formula, the reactive power droop coefficient is in G F1 In the denominator, because D q The static coefficient of the controller, essentially a proportional parameter, should only affect the static output or appear in the gain of the feedback channel. If it's in the denominator, it implies an inertial factor, etc. Furthermore, to further improve and simplify the function structure, it can be... Figure 8 G in F1 Branching is equivalent to Figure 9 G in F2 Branch.
[0127] in Since it is often difficult to implement purely differential elements in actual control systems, it is also important to avoid the occurrence of purely differential elements during the simplification process.
[0128] in
[0129] The final control block diagram is shown above. Figure 10 As shown, the auxiliary branch F is finally obtained after continuously simplifying the rotating positive synchronous torque. This auxiliary branch feeds back the state variables of the reactive power loop to the active power loop. The RPCL simulates the excitation regulator. Its dynamic characteristics can effectively suppress low-frequency oscillations and improve the damping performance of the system, increase the damping torque and thus improve the damping ratio of the system.
[0130] Step 4: Verify the effect of the additional damping branch on suppressing low-frequency oscillations through simulation.
[0131] First, construct a virtual synchronous machine grid-connected simulation model;
[0132] Then, a power step disturbance is applied based on the steady-state condition;
[0133] Finally, the system response with and without additional damping branches is compared to verify the oscillation suppression effect.
[0134] To verify the effectiveness of the aforementioned low-frequency oscillation suppression strategy, a grid-connected simulation model of a virtual synchronizer was established in this embodiment. The simulation platform is based on Simulink / Matlab R2022b, and the parameters of the virtual synchronizer are shown in Table 1 below. The simulation verification steps are as follows: First, the VSG parameters are initially set to P... ref Q ref w0 and E ref After input, the grid connection stabilizes at a steady-state equilibrium point. Then, based on this steady-state equilibrium point, P... ref Or Q ref Perform a step perturbation to make them step to P ref1 Or Q ref1 Finally, we observed and compared the differences in the step response waveforms of the two output variables under the presence and absence of a low-frequency oscillation suppression strategy based on damping torque.
[0135] Table 1. Simulation parameters of the VSG small-signal model
[0136]
[0137]
[0138] In the simulation of the above suppression strategy, K1 = 0.5 was used for comparative simulation experiments. The experimental waveform consisted of active power Pout, reactive power Qout, Evsg, and angular frequency ω. The system reached steady state 5 seconds prior. At 5 seconds, step disturbances were applied to the system for both active and reactive power. The active power reference value jumped from 69.42 W to 124.35 W, and the reactive power reference value jumped from 0 to 30 Var. The simulation results show that the low-frequency oscillation amplitude of the system decreased after applying the suppression strategy of this invention, and the system eventually stabilized. This is consistent with the previous analysis.
[0139] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely preferred examples and are not intended to limit the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.
Claims
1. A method for suppressing low-frequency oscillations in a grid-type inverter based on damping torque, characterized in that, Includes the following steps: S1. Establish a small-signal model of the virtual synchronizer; S101. Select state variables based on the grid connection circuit diagram of the virtual synchronous machine and construct a nonlinear system expression; S102. Introduce a small disturbance at the steady-state equilibrium point and linearize to obtain a linear system in state-space form; S103. Determine the system's output matrix to form a complete small-signal model; S2. Based on the small-signal model, derive the damping torque model; S201. Transform the small-signal model into an equivalent active power control loop block diagram; S202. Identify and separate the synchronous torque and damping torque based on the equivalent active power control loop block diagram. S203. Based on synchronous torque and damping torque, establish a damping torque model and analyze its impact on the dynamic characteristics of the system. S3. Introduce an additional damping branch in the power control loop to enhance the damping torque of the system; S4. The effect of the additional damping branch on suppressing low-frequency oscillations is verified by simulation.
2. The method for suppressing low-frequency oscillations in a grid-type inverter based on damping torque according to claim 1, characterized in that, In S101, the selected state variable is ,in for , The difference in their vector angles; It is the angular frequency of the virtual synchronizer; This serves as a reference for the output voltage amplitude.
3. The method for suppressing low-frequency oscillations in a grid-type inverter based on damping torque according to claim 1, characterized in that, In S101, the expression for the nonlinear system is: ； Define a stable equilibrium point and at a stable equilibrium point Add small perturbations at the location Thus, a linear system is obtained: ； According to the state matrix and input matrix ,Pick The system output is the output quantity, and the system output matrix is obtained. Thus, the final small-signal model is obtained, expressed as follows: 。 4. The method for suppressing low-frequency oscillations in a grid-type inverter based on damping torque according to claim 1, characterized in that, The expression for the synchronous torque is as follows: ； in, It is electromagnetic power. It is the generator power angle; The damping torque is expressed as follows: ； in It is the damping coefficient. It is the rate of change of the work angle.
5. The method for suppressing low-frequency oscillations in a grid-type inverter based on damping torque according to claim 4, characterized in that, The damping torque model expression is as follows: Equivalent positive synchronous torque: ; in, It is synchronous torque. It is the rated angular frequency and the loop equivalent gain. ; Equivalent positive damping torque: ; in, It is the damping torque. .
6. The method for suppressing low-frequency oscillations in a grid-type inverter based on damping torque according to claim 5, characterized in that, S3 includes the following sub-steps: S301. Add a high-pass filter function to the synchronous torque feedback branch to convert the synchronous torque into damping torque; S302. Through equivalent transformation, the additional branch is simplified into a transfer function containing additional coefficients and time constant; S303. The simplified feedback branch is introduced into the active power loop to form an additional damping control structure.
7. The method for suppressing low-frequency oscillations in a grid-type inverter based on damping torque according to claim 6, characterized in that, The expression for the high-pass filter function is as follows: = ； Where K is the gain coefficient, It is the cutoff angular frequency.
8. The method for suppressing low-frequency oscillations in a grid-type inverter based on damping torque according to claim 7, characterized in that, The expression for the transfer function is as follows: ； in, It is the gain coefficient.
9. The method for suppressing low-frequency oscillations in a grid-type inverter based on damping torque according to claim 6, characterized in that, The additional damping control structure formed in S303 is as follows: 。 10. The method for suppressing low-frequency oscillations in a grid-type inverter based on damping torque according to claim 6, characterized in that, The additional damping branch feeds back the state variables of the reactive power loop to the active power loop, simulating the dynamic characteristics of the excitation regulator to enhance system damping.
11. The method for suppressing low-frequency oscillations in a grid-type inverter based on damping torque according to claim 1, characterized in that, S4 includes the following sub-steps: S401. Construct a virtual synchronous machine grid-connected simulation model; S402. Apply a power step disturbance on the steady-state basis; S403. Compare the system response with and without additional damping branches to verify the oscillation suppression effect.