Impedance modeling method and system of grid-forming SVG based on grid connection of wind power

Abstract

The application discloses a grid-connected SVG impedance modeling method and system based on wind power integration, establishes a permanent magnet synchronous fan mathematical model and a converter control strategy, and provides a theoretical basis for impedance characteristic quantization and oscillation analysis; a time domain control structure model of the grid-connected SVG is constructed to clearly indicate the signal transmission relationship among power synchronization control, reactive voltage droop, voltage outer loop and current inner loop; small signal linearization is carried out on the grid-connected SVG, a frequency domain impedance model of the grid-connected SVG in a dq coordinate system is derived, and the frequency domain impedance model is used for small disturbance stability analysis and system strength evaluation of the wind power integration system; the frequency domain impedance model is applied to stability evaluation of the wind power plant connected with a weak power grid, and based on the phase margin of the power grid impedance and the wind power plant impedance, the influence of the working mode of the grid-connected SVG on the system stability is analyzed. The application can effectively quantify the influence of key parameters on the stability by constructing a full control loop small signal impedance model and introducing a wideband system strength evaluation index, and can inhibit wideband oscillation and provide reliable support for wind power integration.

Description

Technical Field

[0001] This invention relates to the field of grid-connected SVG impedance modeling technology, specifically to a grid-connected SVG impedance modeling method and system based on wind power grid connection. Background Technology

[0002] The current energy structure is rapidly transitioning towards low-carbon development, with the installed capacity of new energy sources, represented by permanent magnet direct-drive wind turbines, growing rapidly. Permanent magnet direct-drive wind turbines, with their advantages of gearless operation, high efficiency, and flexible grid connection, are becoming one of the mainstream models for wind power grid connection. However, large-scale integration of new energy sources has also altered the operating characteristics of the power system. Permanent magnet direct-drive wind turbines connect to the grid through full-power converters, flexibly decoupling the rotor from the grid. While this improves speed regulation capabilities, it also leads to a decrease in system inertia and weakened damping. With the increasing penetration rate of wind power, broadband oscillation accidents caused by the impedance interaction between the converter and the grid occur frequently, seriously threatening grid security and hindering the absorption of new energy. To stabilize the voltage at the wind farm grid connection point, static var generators (SVG) have become a core dynamic reactive power compensation device. The grid-following SVG widely used in engineering relies on phase-locked loops to track the grid phase. However, under weak grid or high-penetration conditions, the limitations of grid-connected SVG become apparent: First, the coupling between the phase-locked loop and the grid impedance can easily cause small disturbance instability, and even subsynchronous oscillations may occur when the short-circuit ratio is low; second, it exhibits negative damping characteristics over a wide frequency range, making it prone to resonance with wind turbines and lines, thus limiting the transmission capacity; third, the low-bandwidth voltage control response is slow, making it difficult to quickly provide reactive power support during transient processes, and thus failing to meet the power system's requirements for inertia and active voltage support.

[0003] To overcome the aforementioned shortcomings, grid-connected SVG technology has gradually emerged. It simulates the self-synchronization mechanism of synchronous generators, autonomously constructing its internal potential without a phase-locked loop, exhibiting low-impedance voltage source characteristics, and actively providing virtual inertia and reactive power support. However, grid-connected SVG introduces multi-timescale control mechanisms such as virtual synchronization, reactive power droop, and dual inner loops for voltage and current, making its interaction mechanism with wind power converters and the power grid highly complex. Currently, the impact of key parameters such as virtual inertia and damping coefficient on system stability is unclear, and there is a lack of quantitative models to guide parameter optimization. Existing impedance modeling is mostly for single converters or conventional grid-connected SVGs, and a complete small-signal impedance model covering the entire control loop of grid-connected SVGs has not yet been established, making it impossible to accurately assess the broadband small-disturbance stability of the system after its integration. Therefore, it is urgent to study the impedance frequency characteristics of grid-connected SVGs and establish a small-disturbance stability analysis method suitable for high-penetration direct-drive wind farm grid-connected systems. Summary of the Invention

[0004] To address the problems of incomplete impedance models, lack of theoretical basis for parameter design, and difficulty in assessing broadband stability in existing grid-connected SVG models, this invention provides a method and system for modeling the impedance of grid-connected SVG based on wind power grid connection. By constructing a small-signal impedance model of the entire control loop and introducing broadband system strength evaluation indicators, the method effectively quantifies the impact of key parameters on stability, suppresses broadband oscillations, and provides reliable support for wind power grid connection.

[0005] The technical solution adopted in this invention is as follows: The method for modeling the impedance of grid-connected SVG based on wind power includes the following steps: S1: Establish a mathematical model of a permanent magnet synchronous wind turbine and its converter control strategy to provide a theoretical basis for impedance characteristic quantification and oscillation analysis; S2: Construct a time-domain control structure model for a grid-type SVG to clarify the signal transmission relationships between power synchronization control, reactive voltage droop, voltage outer loop, and current inner loop; S3: Perform small-signal linearization on the grid-type SVG and derive its frequency domain impedance model in the dq coordinate system for small disturbance stability analysis and system strength assessment of wind power grid-connected systems. S4: The frequency domain impedance model is applied to the stability assessment of wind farms connected to weak power grids. Based on the Bode plot phase margin of grid impedance and wind farm impedance, the impact of the grid-type SVG operating mode on system stability is analyzed.

[0006] In S1, the converter control strategy includes machine-side converter control and grid-side converter control. The machine-side converter adopts rotor field-oriented speed outer loop and current inner loop vector control to achieve maximum power point tracking. The grid-side converter adopts a grid voltage-oriented dual closed-loop structure, with the outer loop controlling DC voltage and reactive power and the inner loop controlling current to achieve DC bus voltage stability and independent active and reactive power control.

[0007] In S1, the mathematical model of the permanent magnet synchronous wind turbine includes the stator voltage equation and the stator flux linkage equation, which are expressed in the abc coordinate system as follows: (1); in, (2); In the above formula, , , This refers to the three-phase stator voltage. , , For three-phase stator current, , , For three-phase winding self-inductance, , , For mutual inductance between windings, For armature resistance, , , For three-phase winding flux linkage, For differential operators, It is a permanent magnet flux linkage. , , For each pole of the three-phase winding turn chain, the permanent magnet flux linkage is 1. The mathematical model in the two-phase coordinate system is obtained through polar coordinate transformation: (3); The output electromagnetic torque is: (4); In the above formula, , These are the d-axis and q-axis components of the stator voltage, respectively. , These are the d-axis and q-axis components of the stator current, respectively. , These are direct-axis inductors and quadrature-axis inductors, respectively. Electric angular velocity, To output electromagnetic torque, It is an extreme logarithm.

[0008] S2 includes: 2.1: Establish a small-signal model of the electrical system, taking the direction of current flow to the power grid as the reference direction, and perform a model of the filter inductor in the dq coordinate system. and filter capacitor Linearizing the dynamic equations, we get: (5); in: (6); In the above formula, Indicates a small semaphore, superscript Represents system coordinate system variables; , These are the d-axis and q-axis components of the SVG bridge arm voltage, respectively. , These are the d-axis and q-axis components of the voltage at the point of common coupling, respectively. , These are the d-axis and q-axis components of the SVG bridge arm current, respectively. , These are the d-axis and q-axis components of the SVG network-side current, respectively. The fundamental angular frequency, This is the inductance-impedance matrix; Here is the capacitance admittance matrix; 2.2: A synchronous control loop is constructed based on active power control, and its control equation is as follows: (7); After linearization, the small-signal model is obtained as follows: (8); In the above formula, To control the phase angle, For control coefficients, The inertia coefficient, The damping coefficient is... and These are the reference value and the actual value of active power, respectively. The phase error angle is indicated by the superscript. Indicates the control coordinate system variables; , These represent the steady-state current values ​​of the d-axis and q-axis components, respectively. , These represent the steady-state voltage values ​​of the d-axis and q-axis components, respectively.

[0009] 2.3: Based on the small-signal model of the electrical system, a small-signal model of the reactive power droop element is established, and its control equation is: (9); After linearization, the small-signal model is obtained as follows: (10); In the above formula, This is the reference value for the d-axis voltage. This is the reactive voltage droop factor. and These are the reference value and the actual value of reactive power, respectively. The rated voltage at the point of common coupling; 2.4: The voltage control signal for the network-type SVG bridge arm is generated from the electrical sampling signal through a voltage and current dual closed-loop control. The voltage and current dual closed-loop control equation can be described as: (11); (12); In the above formula, , They are respectively , Corresponding reference value; , These are the proportional coefficient and integral coefficient of the voltage outer loop, respectively. , They are respectively , Corresponding reference value; , These are the proportional coefficient and integral coefficient of the inner current loop, respectively; Based on the aforementioned synchronous control loop, reactive power droop loop, and small-signal model of the electrical system, a dual closed-loop control small-signal model consisting of an outer voltage loop and an inner current loop is established, with the following linearized form: (13); (14); In the above formula, , These are the reference values ​​for the d and q axes of the bridge arm currents, respectively. , These are the PI controller matrices; , These are the cross-decoupling matrices.

[0010] S3 includes: S3.1: Introduce Parker transformation correction between the control coordinate system and the system coordinate system to correct phase error. Substituting into the linearized Park transform and neglecting steady-state signal error and second-order signal error, we obtain the mapping relationship between voltage and current disturbances in the two coordinate systems: (15); (16); (17); (18); In the above formula, , These are the steady-state values ​​of the SVG bridge arm voltages. , These are the steady-state values ​​of the bridge arm currents, respectively. The d-axis small-signal disturbance component represents the voltage at the point of common connection in the system coordinate system. The q-axis small-signal disturbance component represents the voltage at the point of common connection in the system coordinate system. The d-axis small-signal disturbance component represents the SVG arm current in the system coordinate system. This represents the q-axis small-signal disturbance component of the SVG bridge arm current in the system coordinate system.

[0011] S3.2: Substituting the phase error generated by the power synchronization control loop into the above mapping relationship, we obtain the explicit coupling matrix equations for voltage and current disturbances between the control coordinate system and the system coordinate system: (19); (20); (twenty one); (twenty two); In the above formula, This is the coupling matrix from the voltage at the common connection point in the system coordinate system to the voltage command of the bridge arm in the control coordinate system; This is the coupling matrix from the current at the common connection point in the system coordinate system to the voltage command of the bridge arm in the control coordinate system. This is the coupling matrix from the voltage at the common connection point in the system coordinate system to the voltage at the common connection point in the control coordinate system; This is the coupling matrix from the current at the common point of connection in the system coordinate system to the voltage at the common point of connection in the control coordinate system; This is the coupling matrix from the voltage at the common connection point in the system coordinate system to the current in the bridge arm of the control coordinate system. The coupling matrix from the current at the common connection point in the system coordinate system to the current in the bridge arm of the control coordinate system; This is the coupling matrix from the voltage at the common connection point in the system coordinate system to the network-side current in the control coordinate system; The coupling matrix from the current at the common connection point in the system coordinate system to the current on the network side of the control coordinate system; This represents the small-signal disturbance vector of the grid-side current at the point of common coupling in the system coordinate system, expressed by the d-axis. and q-axis It consists of two disturbance components.

[0012] S3.3: By simultaneously establishing the small-signal model and coupling matrix equations of each component and eliminating intermediate variables, the frequency domain impedance model expression of the network-type SVG is obtained as follows: (twenty three); in, This refers to the voltage disturbance at the point of common coupling. This represents the grid-side current disturbance.

[0013] S4 includes: S4.1: Configure a grid-connected SVG with a rated capacity of 10% to 20% of the total capacity of the wind farm in the wind farm, and make it work in constant reactive power control mode. Analyze the amplitude-frequency and phase-frequency characteristics of the overall impedance of the wind farm and the grid impedance through Bode plot analysis to evaluate the stability of the grid-connected system. S4.2: Operate the grid-type SVG in constant voltage control mode, gradually increase the proportional coefficient of its AC voltage outer loop, measure the impedance amplitude-frequency characteristics of the SVG and the overall impedance characteristics of the wind farm under different proportional coefficients, and determine the trend of system stability based on the phase margin at the intersection of the grid impedance and the wind farm impedance amplitude.

[0014] In S4.1, under constant reactive power control mode, the equivalent impedance modulus of the grid-type SVG is much higher than that of the permanent magnet synchronous wind turbine. The overall impedance of the wind farm including the SVG is basically the same as the impedance amplitude-frequency and phase-frequency characteristics of the individual permanent magnet synchronous wind turbine, with only a slight deviation near the fundamental frequency.

[0015] In S4.2, when the proportional coefficient increases from 0.5 to 5.5, the frequency of the intersection point between the wind farm and the grid impedance amplitude with a short-circuit ratio of 2 decreases from 72Hz to about 68Hz, and the system phase margin at this intersection frequency changes from positive to negative.

[0016] It also includes S5: verifying the accuracy of the frequency domain impedance model through time domain simulation and frequency sweep, providing technical support for the stable operation of the grid-connected system of high-penetration permanent magnet synchronous wind farm.

[0017] A grid-connected SVG impedance model system based on wind power grid connection is provided, which includes: The permanent magnet synchronous wind turbine modeling module is used to establish the mathematical model of the permanent magnet synchronous wind turbine and its converter control strategy, providing a theoretical basis for impedance characteristic quantification and oscillation analysis. The modeling module for the time-domain control structure of the network-type SVG is used to construct the time-domain control structure model of the network-type SVG to clarify the signal transmission relationship between power synchronization control, reactive voltage droop, voltage outer loop and current inner loop; The frequency domain impedance model derivation module is used to perform small-signal linearization on the grid-type SVG and derive its frequency domain impedance model in the dq coordinate system for small disturbance stability analysis and system strength assessment of wind power grid-connected systems. The stability assessment module is used to apply the frequency domain impedance model to the stability assessment of wind farms connected to weak power grids. Based on the Bode plot phase margin of grid impedance and wind farm impedance, it analyzes the impact of SVG operating mode on system stability.

[0018] This invention provides a grid-connected SVG impedance modeling method and system based on wind power grid connection, with the following technical advantages: 1) This invention establishes a complete small-signal impedance model that covers multiple time-scale control links such as power synchronization control, reactive voltage droop, voltage outer loop and current inner loop of grid-type SVG. It can accurately reflect the broadband impedance characteristics of grid-type SVG in the dq coordinate system and solve the problem that the impedance model is incomplete and cannot accurately evaluate the broadband small disturbance stability due to the neglect of power synchronization control and double closed-loop coupling in the prior art.

[0019] 2) Based on the frequency domain impedance model, this invention can quantitatively analyze the influence of virtual inertia, damping coefficient, reactive power droop coefficient and voltage and current dual-loop control parameters on the system output impedance and stability margin, providing a theoretical basis for the optimization and tuning of key control parameters of grid-type SVG, and overcoming the blindness of traditional trial-and-error methods that lack quantitative model support.

[0020] 3) This invention adopts a broadband system strength assessment method based on impedance amplitude and phase characteristics and phase margin, which breaks through the limitation that the traditional short-circuit ratio can only reflect the static strength at the power frequency. It can perform a refined assessment of the system strength of subsynchronous, supersynchronous and high-frequency bands, thereby effectively identifying broadband oscillation risk bands.

[0021] 4) By applying the established impedance model to the stability analysis of wind power grid-connected systems, this invention reveals the influence of the AC voltage outer loop proportional coefficient on the system phase margin under constant voltage operation mode of the grid-type SVG, and clarifies the instability boundary where the phase margin changes from positive to negative due to parameter changes. This provides a clear direction for the design of control parameters to suppress subsynchronous oscillations and improve the system damping characteristics.

[0022] 5) Through PSCAD / EMTDC time-domain simulation and impedance frequency sweep verification, this invention proves the high accuracy of the frequency domain impedance model established in this invention. It can effectively reveal the broadband interaction mechanism of grid-connected SVG and permanent magnet direct-drive wind farm, improve the stable operation capability of high-penetration direct-drive wind farms under weak power grids, and provide reliable technical support for the planning and operation of new energy power systems. Attached Figure Description

[0023] The present invention will be further described below with reference to the accompanying drawings and examples; Figure 1 This is the equivalent circuit diagram of the permanent magnet synchronous fan in this invention; Figure 2(a) is a schematic diagram of the control strategy of the permanent magnet synchronous wind turbine converter in this invention (machine-side converter control). Figure 2(b) is a schematic diagram of the control strategy of the permanent magnet synchronous wind turbine converter in this invention (grid-side converter control). Figure 3 This is the impedance characteristic curve of the wind farm grid-connected system under the constant reactive power control mode of the grid-type SVG in this invention.

[0024] Figure 4 This is the impedance characteristic curve of the wind farm grid-connected system under the constant voltage control mode of the grid-type SVG in this invention.

[0025] Figure 5 This is the impedance verification result of the mesh-type SVG in this invention.

[0026] Figure 6(a) shows the phase space trajectory of the grid-type direct-drive fan in this invention; Figure 6(b) shows the phase space trajectory of the grid-type direct-drive fan in this invention.

[0027] Figure 7(a) is a waveform diagram of the grid-side current under the condition of sudden increase in wind power in this invention.

[0028] Figure 7(b) is a fast Fourier transform analysis diagram of the grid-side current under the condition of sudden increase in wind power in this invention. Detailed Implementation

[0029] A method and system for modeling grid-connected SVG impedance based on wind power grid connection, the method including the following steps: S1: Establish a mathematical model of a permanent magnet synchronous wind turbine and its converter control strategy to provide a theoretical basis for subsequent impedance characteristic quantification and oscillation analysis in conjunction with SVG; S2: Construct a time-domain control structure model for a grid-type SVG, and clarify the signal transmission relationship between its power synchronization control, reactive voltage droop, voltage outer loop, and current inner loop; S3: Perform small-signal linearization on the grid-type SVG and derive its frequency domain impedance model in the dq coordinate system for small disturbance stability analysis and system strength assessment of wind power grid-connected systems. S4: The established frequency domain impedance model is applied to the stability assessment of the wind farm connected to the weak power grid. Based on the Bode plot phase margin of the grid impedance and the wind farm impedance, the impact of the SVG operating mode on the system stability is analyzed.

[0030] As a preferred embodiment, the method further includes S5: verifying the accuracy of the frequency domain impedance model through PSCAD / EMTDC time-domain simulation and frequency sweeping, providing technical support for the stable operation of the grid-connected system of a high-penetration permanent magnet synchronous wind farm.

[0031] S1: Mathematical model of permanent magnet synchronous wind turbine and converter control strategy: A permanent magnet synchronous fan can be simplified as an ideal motor. Assuming the permanent magnet flux is constant and the induced electromotive force is a sinusoidal waveform, its equivalent circuit is as follows: Figure 1 As shown. Figure 1 middle, , , This refers to the three-phase stator voltage. , , For three-phase stator current, , , For three-phase winding self-inductance, , , For mutual inductance between windings, Let be the armature resistance. The mathematical models of the stator voltage equation and stator flux linkage equation in the abc coordinate system are as follows: (1); in, (2); in, , , For three-phase winding flux linkage; It is a differential operator; It is a permanent magnet flux linkage. , , It is the permanent magnet flux linkage per pole of the three-phase winding turn chain.

[0032] To simplify the analysis, the mathematical model in the three-phase coordinate system is transformed to the two-phase rotating coordinate system using polar coordinate transformation, resulting in: (3); In the formula, , The stator voltage has d-axis and q-axis components. , These are the d-axis and q-axis components of the stator current. , These are direct-axis inductors and quadrature-axis inductors, respectively. Let be the electric angular velocity. The equation for the output electromagnetic torque is: (4); in, To output electromagnetic torque; It is an extreme logarithm.

[0033] The permanent magnet synchronous wind turbine converter adopts a dual-converter structure consisting of a machine-side converter and a grid-side converter. The machine-side and grid-side converters jointly achieve maximum power point tracking (MPPT), DC bus voltage stability, and independent control of grid-connected active and reactive power. Its control strategy is shown in Figures 2(a) and 2(b). Figure 2(a) is the control block diagram of the machine-side converter, which achieves MPPT by adjusting the electromagnetic torque. It employs rotor field-oriented vector control, consisting of an outer speed loop and an inner current loop. In the outer speed loop, the speed reference value... The deviation from the actual rotational speed is used to obtain the q-axis current reference value through PI control. Simultaneously set the d-axis current reference value. To decouple torque from flux linkage. The inner current loop d-axis channel will... Compared with actual value The deviation is adjusted by a PI controller to obtain the initial voltage, and then the cross-decoupling term is subtracted. Post-output command voltage The q-axis channel will Compared with actual value The deviation is adjusted by a PI controller to obtain the initial voltage, and then a cross-decoupling term is added. and back electromotive force Post-output command voltage . , Switching signals are generated through coordinate transformation and pulse width modulation.

[0034] Figure 2(b) shows the control block diagram of the grid-side converter, which adopts a grid voltage-oriented double closed-loop structure. The outer loop controls the DC voltage and reactive power, while the inner loop controls the current. The outer loop controls the actual value of the DC bus voltage. Compared with reference value The deviation is adjusted by PI to obtain the current d-axis reference value. The reactive power outer loop will display the actual value of the reactive power output by the wind turbine. Its reference value The deviation is adjusted by PI to obtain the current q-axis reference value. The inner current loop divides the grid-side current into d-axis and q-axis components respectively. , track , The deviation is adjusted by a PI controller to obtain the command voltage output of the inner current loop. , Then superimpose cross-decoupling terms , And voltage feedforward to obtain the modulation voltage , The converter is driven after coordinate transformation and pulse width modulation. This control strategy jointly realizes the maximum power point tracking of the permanent magnet synchronous wind turbine, DC bus voltage stability, and independent control of grid-connected active and reactive power, laying a theoretical foundation for subsequent impedance characteristic quantification and oscillation analysis of parallel systems.

[0035] S2: Construction of a network-type SVG time-domain control structure model: The grid-type SVG simulates the self-synchronization mechanism of a synchronous generator, which can autonomously construct its internal potential without a phase-locked loop, exhibiting low-impedance voltage source characteristics and actively providing virtual inertia and reactive power support. Its control structure mainly includes an electrical system, a synchronization control loop, a reactive power droop loop, and a voltage-current dual closed loop. Small-signal models are established for each part below to clarify the signal transmission relationships.

[0036] (1) Small-signal model of electrical system: Taking the direction of current flow towards the power grid as the system reference direction, the SVG output filter inductor is considered in the dq coordinate system. and filter capacitor Linearizing the dynamic equations, we obtain: (5); in: (6); In the formula, The superscript indicates the small-signal disturbance of the corresponding variable. Represents variables in the system coordinate system; , These are the d-axis and q-axis components of the SVG bridge arm voltage, respectively. , These are the d-axis and q-axis components of the voltage at the point of common coupling, respectively. , These are the d-axis and q-axis components of the SVG bridge arm current, respectively. , These are the d-axis and q-axis components of the SVG grid-side current, respectively. The fundamental angular frequency; This is the inductance-impedance matrix; This is the capacitance admittance matrix. This model describes the dynamic constraint relationships between the inductance, capacitance, voltage, and current within the SVG.

[0037] (2) Synchronization control link: The synchronous control loop of the grid-type SVG simulates the rotor motion equation of a synchronous generator and generates the control phase angle through active power deviation. To achieve self-synchronization with the power grid, its control equation can be expressed as: (7); in, For control coefficients; The inertia coefficient is used to provide virtual inertia support; This is the damping coefficient, used to suppress power oscillations; , These represent the reference and actual active power values ​​output by the SVG, respectively. By performing small-signal linearization on this equation and neglecting steady-state disturbances, the phase error angle can be obtained. This refers to the phase deviation between the control coordinate system and the system coordinate system, expressed as: (8); Among them, superscript Indicates the control coordinate system variables; , , , These represent the steady-state values ​​of the grid-side current and voltage along the d and q axes, respectively. This phase error... This is the key to subsequent coordinate transformation coupling, reflecting the core impact of grid-type SVG power synchronization control on impedance characteristics.

[0038] (3) Unreacted drooping phase: Reactive power droop control is used to simulate the excitation regulation characteristics of a synchronous generator. It adjusts the voltage reference value by controlling the reactive power deviation, enabling the SVG to have autonomous voltage support capability. Its control equation is as follows: (9); In the formula, This is the reference value for the d-axis voltage. This is the reactive voltage droop factor; , These are the reference and actual reactive power values ​​output by the SVG, respectively. Let be the rated voltage at the point of common coupling. Linearizing this equation yields the small-signal model: (10); This formula shows that the reactive power droop introduces grid-side voltage and current disturbances into the voltage reference value, thereby affecting the command signal of the outer voltage loop.

[0039] (4) Voltage control loop and current control loop: The voltage control signal for the network-type SVG bridge arm is generated from the electrical sampling signal through a voltage and current dual closed-loop control. The voltage and current dual closed-loop control equation can be described as: (11); (12); In the above formula, , They are respectively , Corresponding reference value; , These are the proportional coefficient and integral coefficient of the voltage outer loop, respectively. , They are respectively , Corresponding reference value; , These are the proportional coefficient and integral coefficient of the inner current loop, respectively; Based on the aforementioned synchronous control loop, reactive power droop loop, and small-signal model of the electrical system, a dual closed-loop control small-signal model consisting of an outer voltage loop and an inner current loop is established, with the following linearized form: (13); (14); In the above formula, , These are the reference values ​​for the d and q axes of the bridge arm currents, respectively. , These are the PI controller matrices; , These are cross-decoupling matrices, containing decoupling terms introduced by filter capacitors or filter inductors. Dual closed-loop control of voltage and current ensures the fast tracking performance of the SVG output voltage, while also transmitting disturbances in the common coupling point voltage and current to the bridge arm voltage command via the control loop.

[0040] S3: Derivation of the frequency domain impedance model for mesh-type SVG: When the system is disturbed, the phase generated by the grid-type SVG through power synchronization control The dynamic changes cause the control coordinate system and the system coordinate system to no longer coincide. To correctly correlate the disturbance components in the two coordinate systems, a Parker transformation correction must be introduced. Ignoring the steady-state signal error and second-order signal error in the two rotating coordinate systems, the phase error is... Substituting into the linearized Park transform, we obtain the mapping relationship between voltage and current disturbances in the two coordinate systems: (15); (16); (17); (18); in, , This represents the steady-state value of the SVG bridge arm voltage. , This represents the steady-state value of the SVG bridge arm current.

[0041] The phase error generated by the synchronization control in step S2 Substituting into the Parker transform linearization equation above, we obtain the explicit coupling relationship between voltage and current disturbances between the control coordinate system and the system coordinate system: (19); (20); (twenty one); (twenty two); Among them, each The matrix is ​​a coupling matrix, the specific form of which is determined by the steady-state operating point and control parameters. It maps voltage and current disturbances in the system coordinate system to the arm voltage command, point of common coupling voltage, arm current, and grid-side current in the control coordinate system, respectively. For example, This is the coupling matrix from the voltage at the common connection point in the system coordinate system to the voltage command of the bridge arm in the control coordinate system. This includes the coupling matrix from the current at the common connection point in the system coordinate system to the voltage command of the bridge arm in the control coordinate system.

[0042] By establishing the small-signal model of the combined electrical system, the linearized equations of each control element, and the aforementioned coordinate transformation coupling matrix, and eliminating intermediate variables, the frequency domain impedance model expression of the network-type SVG can finally be obtained as follows: (twenty three); in, This refers to the voltage disturbance at the point of common coupling. This represents the grid-side current disturbance. The impedance model is a 2×2 matrix, which fully characterizes the broadband impedance characteristics of the grid-type SVG in the dq coordinate system. It quantitatively includes the contributions of various components such as power synchronization control, reactive power droop, and voltage and current dual closed loops. It can be directly used to analyze the interactive oscillation mechanism and small disturbance stability of the SVG and grid impedance.

[0043] S4: Grid-connected stability assessment of wind farms: Based on the aforementioned frequency domain impedance model, the small-disturbance stability assessment of wind farm grid-connected systems with grid-type SVG can be performed. In wind farms, SVG typically employs grid-type control to undertake reactive power compensation tasks, and its rated capacity is generally configured at 10% to 20% of the total wind farm capacity.

[0044] Figure 3 The impedance-frequency characteristic curves of the SVG (Static Var Generator) operating in constant reactive power control mode are shown in a wind farm with a grid-type SVG. From Figure 3 As can be seen, the equivalent impedance modulus of the SVG in this mode is much higher than that of the permanent magnet synchronous wind turbine. From the amplitude-frequency and phase-frequency characteristics, the overall impedance of the wind farm including the SVG is basically the same as that of a single permanent magnet synchronous wind turbine, with only a slight deviation near the fundamental frequency. This indicates that under constant reactive power mode, grid-connected SVG does not significantly change the system's impedance characteristics. The system stability is mainly determined by the permanent magnet synchronous wind turbine, with the SVG primarily providing reactive power compensation, and it does not introduce new oscillation risks.

[0045] However, when the SVG operates in constant voltage control mode, the influence of its AC voltage outer loop on the impedance characteristics will be reflected in the denominator of the SVG impedance expression, and changes in control parameters may significantly alter the system impedance. To investigate this effect, keeping other conditions constant, the proportional coefficient of the SVG AC voltage outer loop was gradually increased. The impedance amplitude-frequency characteristics of the SVG and the overall impedance characteristics of the wind farm were measured under different scaling factors. The results are as follows: Figure 4 As shown. When As the value increases from 0.5 to 5.5, the frequency of the intersection point between the wind farm and the grid impedance amplitude with a short-circuit ratio of 2 gradually decreases from 72Hz to about 68Hz, and at the same time, the system phase margin at this intersection frequency changes from positive to negative.

[0046] According to the Nyquist stability criterion, the small disturbance stability of a grid-connected system depends on the ratio of the grid impedance to the wind farm impedance. When the amplitude-frequency curves of the two intersect, if the phase difference at the intersection frequency is less than 180°, that is, the phase margin is positive, the system is stable; otherwise, if the phase margin is negative, the system will experience oscillation and instability.

[0047] The experimental results above show that the AC voltage outer loop scaling factor of the SVG in constant voltage mode has a significant impact on the impedance characteristics of the grid-connected system. An excessively large scaling factor will lead to a decrease in phase margin, which may in turn cause subsynchronous oscillations. Using the frequency domain impedance model established in this invention, virtual inertia can be quantitatively analyzed. Damping coefficient reactive power droop coefficient The study also investigated the influence of voltage and current loop parameters on phase margin, providing a theoretical basis for optimizing the tuning of control parameters for grid-type SVG and effectively avoiding the blindness of traditional trial-and-error methods. Furthermore, this evaluation method overcomes the limitation that the traditional short-circuit ratio can only reflect the static strength at power frequency, achieving a refined evaluation of the strength of subsynchronous, supersynchronous, and high-frequency systems.

[0048] S5: Time-domain simulation and frequency sweep verification: To verify the accuracy of the established frequency domain impedance model, a typical wind farm grid connection model was built based on the PSCAD / EMTDC simulation platform to conduct time-domain simulation and frequency sweep verification of the impact of grid-type SVG access on system stability.

[0049] Figure 5 The impedance verification results of the grid-type SVG are presented. By injecting harmonic disturbances of different frequencies into the grid connection point and performing frequency sweeping, the voltage and current responses of the SVG ports were measured, and the measured impedance characteristics were calculated. As can be seen from the figure, the amplitude-frequency and phase-frequency characteristics of the impedance model derived theoretically are in high agreement with the frequency sweep measurement results, which fully demonstrates the accuracy of the small-signal dq impedance model established in this invention. This model can accurately reflect the impedance frequency characteristics of the grid-type SVG over a wide frequency range.

[0050] Further, taking the operation of an unloaded line under strong winds as an example, the phase space trajectories of grid-type and grid-following type permanent magnet synchronous wind turbines are compared, as shown in Figures 6(a) and 6(b). For the grid-following structure, after the unloaded line is put into operation, a limit cycle centered on the stable equilibrium point appears between the active and reactive currents. The reactive current fluctuates violently, the reactive compensation behavior of the SVG lacks determinism, and the system exhibits continuous oscillation with constant amplitude, indicating an unstable state. However, when the permanent magnet synchronous wind turbine adopts a grid-type structure, the phase trajectories of the two state variables gradually converge from the initial point to the equilibrium point, and the time-domain response shows that the system can recover stable operation. Therefore, it can be seen that the grid-type structure has a significant suppressive effect on the continuous oscillation phenomenon that occurs under strong winds.

[0051] To verify the response characteristics of a parallel system of a permanent magnet synchronous wind turbine and a grid-connected SVG under weak grid conditions to a sudden increase in wind power, the input active power of the permanent magnet synchronous wind turbine was stepped from 0.8 pu to 0.98 pu at 7 s. Figure 7(a) shows the time-domain waveform of the grid-side current under this condition. It can be seen that after the system experiences a power step disturbance, the grid-side current quickly recovers to a stable operating state after only about a quarter of the power frequency cycle, without constant amplitude oscillation or instability. This indicates that the parallel system has good dynamic response speed and disturbance resistance to sudden increases in wind power. Figure 7(b) shows the fast Fourier transform analysis results of the current under the corresponding condition. The total harmonic distortion rate of the current is only 1.01%, which meets the power quality requirements.

[0052] The above time-domain simulation and frequency sweep verification results fully demonstrate that the frequency domain impedance model of the grid-type SVG established in this invention is accurate and reliable, and can effectively reveal the broadband interaction mechanism between the grid-type SVG and the grid-connected permanent magnet synchronous wind farm system, providing important theoretical analysis tools and technical support for the stable operation of the grid-connected high-penetration permanent magnet synchronous wind farm system.

[0053] In summary, this invention addresses the problems of traditional grid-connected SVG (Static Var Generator) systems, such as reliance on phase-locked loops, instability under weak grid conditions, and incomplete impedance models, by establishing a complete small-signal impedance model covering multiple time-scale control components including power synchronization control of grid-connected SVG, reactive voltage droop, voltage outer loop, and current inner loop. Based on this model, the impact of key control parameters on system output impedance and stability can be quantitatively analyzed, overcoming the blindness of traditional trial-and-error methods. Furthermore, this invention, based on a broadband evaluation method using impedance ratio and phase margin, achieves a refined evaluation of system strength across the entire frequency band. This effectively reveals the broadband interaction mechanism between grid-connected SVG and permanent magnet synchronous wind farm grid-connected systems, suppresses subsynchronous oscillations, improves system damping characteristics, and significantly enhances the stable operation capability of high-penetration permanent magnet synchronous wind farms under weak grid conditions.

Claims

1. A grid-connected SVG impedance modeling method based on wind power grid connection, characterized in that... Includes the following steps: S1: Establish a mathematical model of a permanent magnet synchronous wind turbine and its converter control strategy; S2: Construct a time-domain control structure model for a grid-type SVG to clarify the signal transmission relationships between power synchronization control, reactive voltage droop, voltage outer loop, and current inner loop; S3: Perform small-signal linearization on the grid-type SVG and derive its frequency domain impedance model in the dq coordinate system for small disturbance stability analysis and system strength assessment of wind power grid-connected systems. S4: Apply the frequency domain impedance model to the stability assessment of wind farms connected to weak power grids. Based on the phase margin of grid impedance and wind farm impedance, analyze the impact of the grid-type SVG operating mode on system stability.

2. The method for modeling grid-connected SVG impedance based on wind power grid connection according to claim 1, characterized in that: In S1, the converter control strategy includes machine-side converter control and grid-side converter control. The machine-side converter adopts rotor field-oriented speed outer loop and current inner loop vector control to achieve maximum power point tracking. The grid-side converter adopts a grid voltage-oriented dual closed-loop structure, with the outer loop controlling DC voltage and reactive power and the inner loop controlling current to achieve DC bus voltage stability and independent active and reactive power control.

3. The grid-connected SVG impedance modeling method based on wind power grid connection according to claim 2, characterized in that: In S1, the mathematical model of the permanent magnet synchronous wind turbine includes the stator voltage equation and the stator flux linkage equation, which are expressed in the abc coordinate system as follows: （1）； in, （2）； In the above formula, , , This refers to the three-phase stator voltage. , , For three-phase stator current, , , For the self-inductance of the three-phase winding, , , For mutual inductance between windings, For armature resistance, , , For three-phase winding flux linkage, For differential operators, It is a permanent magnet flux linkage. , , For each pole of the three-phase winding turn chain, the permanent magnet flux linkage is 1. The mathematical model in the two-phase coordinate system is obtained through polar coordinate transformation: （3）； The output electromagnetic torque is: （4）； In the above formula, , These are the d-axis and q-axis components of the stator voltage, respectively. , These are the d-axis and q-axis components of the stator current, respectively. , These are direct-axis inductors and quadrature-axis inductors, respectively. Electric angular velocity, To output electromagnetic torque, It is an extreme logarithm.

4. The grid-connected SVG impedance modeling method based on wind power grid connection according to claim 3, characterized in that: S2 includes: 2.1: Establish a small-signal model of the electrical system, taking the direction of current flow to the power grid as the reference direction, and perform a model of the filter inductor in the dq coordinate system. and filter capacitor Linearizing the dynamic equations, we get: （5）； in: （6）； In the above formula, Indicates a small semaphore, superscript Represents system coordinate system variables; , These are the d-axis and q-axis components of the SVG bridge arm voltage, respectively. , These are the d-axis and q-axis components of the voltage at the point of common coupling, respectively. , These are the d-axis and q-axis components of the SVG bridge arm current, respectively. , These are the d-axis and q-axis components of the SVG network-side current, respectively. The fundamental angular frequency, This is the inductance-impedance matrix; Here is the capacitance admittance matrix; 2.2: A synchronous control loop is constructed based on active power control, and its control equation is as follows: （7）； After linearization, the small-signal model is obtained as follows: （8）； In the above formula, To control the phase angle, For control coefficients, The inertia coefficient, The damping coefficient is... and These are the reference value and the actual value of active power, respectively. The phase error angle is indicated by the superscript. Indicates the control coordinate system variables; , These represent the steady-state current values ​​of the d-axis and q-axis components, respectively. , These represent the steady-state voltage values ​​of the d-axis and q-axis components, respectively. 2.3: Based on the small-signal model of the electrical system, a small-signal model of the reactive power droop element is established, and its control equation is: （9）； After linearization, the small-signal model is obtained as follows: （10）； In the above formula, This is the reference value for the d-axis voltage. This is the reactive voltage droop factor. and These are the reference value and the actual value of reactive power, respectively. The rated voltage at the point of common coupling; 2.4: The voltage control signal of the SVG bridge arm in a grid-type structure is generated from the electrical sampling signal through a voltage and current dual closed-loop control; the voltage and current dual closed-loop control equation can be described as: （11）； （12）； In the above formula, , They are respectively , Corresponding reference value; , These are the proportional coefficient and integral coefficient of the voltage outer loop, respectively. , They are respectively , Corresponding reference value; , These are the proportional coefficient and integral coefficient of the inner current loop, respectively; Based on the aforementioned synchronous control loop, reactive power droop loop, and small-signal model of the electrical system, a dual closed-loop control small-signal model consisting of an outer voltage loop and an inner current loop is established, with the following linearized form: （13）； （14）； In the above formula, , These are the reference values ​​for the d and q axes of the bridge arm currents, respectively. , These are the PI controller matrices; , These are the cross-decoupling matrices.

5. The grid-connected SVG impedance modeling method based on wind power grid connection according to claim 4, characterized in that: S3 includes: S3.1: Introduce Parker transformation correction between the control coordinate system and the system coordinate system to correct phase error. Substituting into the linearized Park transform and neglecting steady-state signal error and second-order signal error, we obtain the mapping relationship between voltage and current disturbances in the two coordinate systems: （15）； （16）； （17）； （18）； In the above formula, , These are the steady-state values ​​of the SVG bridge arm voltages. , These are the steady-state values ​​of the bridge arm currents, respectively. The d-axis small-signal disturbance component represents the voltage at the point of common connection in the system coordinate system. The q-axis small-signal disturbance component represents the voltage at the point of common connection in the system coordinate system. The d-axis small-signal disturbance component represents the SVG arm current in the system coordinate system. The q-axis small-signal disturbance component represents the SVG arm current in the system coordinate system. S3.2: Substituting the phase error generated by the power synchronization control loop into the above mapping relationship, we obtain the explicit coupling matrix equations for voltage and current disturbances between the control coordinate system and the system coordinate system: （19）； （20）； （21）； （22）； In the above formula, This is the coupling matrix from the voltage at the common connection point in the system coordinate system to the voltage command of the bridge arm in the control coordinate system; This is the coupling matrix from the current at the common connection point in the system coordinate system to the voltage command of the bridge arm in the control coordinate system. This is the coupling matrix from the voltage at the common connection point in the system coordinate system to the voltage at the common connection point in the control coordinate system; This is the coupling matrix from the current at the common point of connection in the system coordinate system to the voltage at the common point of connection in the control coordinate system; This is the coupling matrix from the voltage at the common connection point in the system coordinate system to the current in the bridge arm of the control coordinate system. The coupling matrix from the current at the common connection point in the system coordinate system to the current in the bridge arm of the control coordinate system; This is the coupling matrix from the voltage at the common connection point in the system coordinate system to the network-side current in the control coordinate system; The coupling matrix from the current at the common connection point in the system coordinate system to the current on the network side of the control coordinate system; This represents the small-signal disturbance vector of the grid-side current at the point of common coupling in the system coordinate system, expressed by the d-axis. and q-axis It consists of two disturbance components; S3.3: By simultaneously establishing the small-signal model and coupling matrix equations of each component and eliminating intermediate variables, the frequency domain impedance model expression of the network-type SVG is obtained as follows: （23）； in, This is the voltage disturbance at the point of common coupling. This represents the grid-side current disturbance.

6. The grid-connected SVG impedance modeling method based on wind power grid connection according to claim 5, characterized in that: S4 includes: S4.1: Configure a grid-connected SVG with a rated capacity of 10% to 20% of the total capacity of the wind farm in the wind farm, and make it work in constant reactive power control mode. Analyze the amplitude-frequency and phase-frequency characteristics of the overall impedance of the wind farm and the grid impedance through Bode plot analysis to evaluate the stability of the grid-connected system. S4.2: Operate the grid-type SVG in constant voltage control mode, gradually increase the proportional coefficient of its AC voltage outer loop, measure the impedance amplitude-frequency characteristics of the SVG and the overall impedance characteristics of the wind farm under different proportional coefficients, and determine the trend of system stability based on the phase margin at the intersection of the grid impedance and the wind farm impedance amplitude.

7. The grid-connected SVG impedance modeling method based on wind power grid connection according to claim 6, characterized in that: In S4.1, under constant reactive power control mode, the equivalent impedance modulus of the grid-type SVG is much higher than that of the permanent magnet synchronous wind turbine. The overall impedance of the wind farm including the SVG is basically the same as the impedance amplitude-frequency and phase-frequency characteristics of the individual permanent magnet synchronous wind turbine, with only a slight deviation near the fundamental frequency.

8. The grid-connected SVG impedance modeling method based on wind power grid connection according to claim 7, characterized in that: In S4.2, when the proportional coefficient increases from 0.5 to 5.5, the frequency of the intersection point between the wind farm and the grid impedance amplitude with a short-circuit ratio of 2 decreases from 72Hz to about 68Hz, and the system phase margin at this intersection frequency changes from positive to negative.

9. The grid-connected SVG impedance modeling method based on wind power grid connection according to claim 8, characterized in that: It also includes S5: verifying the accuracy of the frequency domain impedance model through time domain simulation and frequency sweep, providing technical support for the stable operation of the grid-connected system of high-penetration permanent magnet synchronous wind farm.

10. A grid-connected SVG impedance model system based on wind power grid connection, characterized in that... The system includes: The permanent magnet synchronous wind turbine modeling module is used to establish the mathematical model of the permanent magnet synchronous wind turbine and its converter control strategy, providing a theoretical basis for impedance characteristic quantification and oscillation analysis. The modeling module for the time-domain control structure of the network-type SVG is used to construct the time-domain control structure model of the network-type SVG to clarify the signal transmission relationship between power synchronization control, reactive voltage droop, voltage outer loop and current inner loop; The frequency domain impedance model derivation module is used to perform small-signal linearization on the grid-type SVG and derive its frequency domain impedance model in the dq coordinate system for small disturbance stability analysis and system strength assessment of wind power grid-connected systems. The stability assessment module is used to apply the frequency domain impedance model to the stability assessment of wind farms connected to weak power grids. Based on the Bode plot phase margin of grid impedance and wind farm impedance, it analyzes the impact of SVG operating mode on system stability.

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