A method and system for suppressing subsynchronous oscillation of a virtual synchronous doubly-fed wind turbine connected to the grid through series compensation

Abstract

The invention discloses a method and a system for suppressing subsynchronous oscillation of a virtual synchronous doubly-fed wind turbine connected to the grid through series compensation. The method includes: obtaining an expression of the output impedance of the grid-side converter based on VSG; revealing the positive damping characteristic of the grid-side converter based on VSG for subsynchronous oscillation from the perspective of the equivalent impedance of the doubly-fed wind turbine grid-connected system; analyzing the mechanism of suppressing subsynchronous oscillation of the virtual synchronous doubly-fed wind turbine grid-connected system in combination with active disturbance rejection control; and constructing an improved active disturbance rejection controller to suppress subsynchronous oscillation. The subsynchronous oscillation analysis method adopted by the invention has a certain universality and can provide a theoretical analysis basis for the subsynchronous oscillation problem caused by a high proportion of power electronic devices participating in the new energy power generation system. At the same time, the suppression method proposed by the invention is not only applicable to doubly-fed generating units, but also applicable to suppressing subsynchronous oscillation in direct-drive wind turbines and weak AC systems extended thereto.

Description

Technical field

[0001] The invention relates to a method and a system for suppressing subsynchronous oscillation of a virtual synchronous doubly-fed wind turbine connected to the grid through series compensation, belonging to the field of renewable energy power generation systems. Background technique

[0002] The virtual synchronous generator (VSG) simulates the inertia and frequency response characteristics of the synchronous generator, and can overcome the disadvantages of low inertia and weak damping existing in the high-proportion power electronic wind power generation system. Among them, the virtual synchronous doubly-fed wind turbine has broad application prospects due to its active support for the dynamic changes of inertia and frequency. However, the access of virtual synchronous control makes the interaction characteristics between the doubly-fed wind turbine and the power grid more complex, exacerbates the dynamic characteristics of subsynchronous oscillation of the system, and affects the stability level of subsynchronous oscillation of the system. Therefore, it is urgent to construct a subsynchronous oscillation suppression strategy suitable for the virtual synchronous doubly-fed wind turbine grid-connected system to improve the safe and stable operation ability of the wind power system.

[0003] Regarding the existing research on the subsynchronous oscillation suppression strategy for wind power systems, a large number of literatures have carried out analyses in aspects such as parameter optimization, oscillation filtering, and additional damping. Parameter optimization mainly optimizes and tunes the parameters of the power electronic converter, which can effectively increase the damping of the system at the resonant frequency, thereby avoiding the oscillation instability of the system. However, it is restricted by the requirements of the stable operation boundary of the unit, and the adjustable range of the control parameters of the wind turbine converter is limited. Oscillation filtering mainly designs a band-pass filter or a control structure with filtering effect in the control part to filter out the subsynchronous oscillation components contained in the control link, and then eliminate the machine-network interaction coupling effect in the subsynchronous oscillation frequency band. However, the parameters of such filtering structures are designed for a certain fixed resonant frequency point and are only applicable to a single oscillation scenario. If the grid operating conditions change, this suppression strategy is difficult to effectively maintain the stable operation of the system. Additional damping mostly introduces an additional damping controller in the converter control link to increase the system damping to achieve the purpose of suppressing oscillation. The disadvantage of this type of suppression strategy is that the design link of the additional damping process is more complicated, and once the system working conditions change, the parameters of the additional damping controller need to be reset. Therefore, it is of great practical significance to propose a multi-condition wind turbine oscillation suppression strategy for wind power transmission. In addition, the existing control strategies mostly focus on the design of traditional doubly-fed wind turbines, and there are significant differences between the control structures of virtual synchronous doubly-fed wind turbines and traditional wind turbines. Therefore, the design ideas of the control strategies are also different. Therefore, it is urgent to solve the problem of suppressing subsynchronous oscillation of virtual synchronous doubly-fed wind turbines applicable to multiple working conditions.

[0004] At present, many scholars' research on the dynamic characteristics of VSG mainly focuses on the small-signal stability analysis at the equipment level of virtual synchronous control after the simplification of the control model, the reconstruction of the control strategy, and the optimization of the control parameters. Some scholars have designed a simplified equivalent model of a synchronous generator based on a VSG converter, taking into account the dynamic characteristics and operating standards of the synchronous machine. Some scholars have proposed a low-voltage ride-through control strategy based on VSG, which is easy to analyze the stability of a multi-terminal high-voltage DC system with a voltage-source converter, enabling the grid-side voltage-source converter to provide frequency support and oscillation damping. Some scholars have introduced a frequency change parameter into the active power loop control and tuned the VSG grid-connected parameters by means of adaptive inertia control, improving the dynamic frequency regulation ability of the power grid, but the parameter design process is relatively complex. In summary, the existing literature lacks a reasonable clarification of the inducement of subsynchronous oscillation in virtual synchronous doubly-fed wind turbines, making it difficult to effectively suppress system oscillation from the source. Summary of the Invention

[0005] The present invention provides a method and a system for suppressing subsynchronous oscillation in a virtual synchronous doubly-fed wind turbine connected to the grid through series compensation. Starting from the analysis of the subsynchronous oscillation generation mechanism of this system under VSG control, and combining with the active disturbance rejection control to analyze the subsynchronous oscillation suppression mechanism of the virtual synchronous doubly-fed wind turbine grid-connected system, an improved active disturbance rejection controller that conforms to the above mechanism is constructed; further, the stability of the designed improved active disturbance rejection controller is discussed; and further, different operating conditions are designed to verify the robustness of the suppression strategy proposed by the present invention.

[0006] The technical solution of the present invention is: a method for suppressing subsynchronous oscillation in a virtual synchronous doubly-fed wind turbine connected to the grid through series compensation, including: obtaining an expression of the output impedance of the grid-side converter based on VSG; revealing the positive damping characteristic of the grid-side converter based on VSG for subsynchronous oscillation from the perspective of the equivalent impedance of the doubly-fed wind turbine grid-connected system; analyzing the subsynchronous oscillation suppression mechanism of the virtual synchronous doubly-fed wind turbine grid-connected system in combination with the active disturbance rejection control; and constructing an improved active disturbance rejection controller to suppress subsynchronous oscillation.

[0007] The obtaining of the expression of the output impedance of the grid-side converter based on VSG includes:

[0008] S1.1. Using the small-signal stability analysis method of the power system, linearize the dynamic equation of VSG based on its control topology structure, and the mathematical expression of the linearized result is:

[0009]

[0010] Among them, F PQ 、F PI 、 F1, F2, F L are all 2×2 order transfer function matrices; T J and Dp are the moment of inertia and the damping coefficient respectively; K p and K i are the excitation control proportional coefficient and the integral coefficient respectively; K v is the reactive power-voltage control droop coefficient; s is the Laplace operator; K Vp1 and K Vi1 are the d-axis proportional coefficient and the integral coefficient of the VSG output voltage control respectively; K Vp2 and K Vi2 are the q-axis proportional coefficient and the integral coefficient of the VSG output voltage control respectively; I sd and I sq are the d-axis component and the q-axis component of the steady-state quantity of the stator current in the synchronous rotating coordinate system respectively; U sd and U sq are the d-axis component and the q-axis component of the steady-state operating point of the stator voltage in the synchronous rotating coordinate system respectively; E m is the excitation control output voltage; δ is the difference between the phase angle output by the phase-locked loop and the phase of the grid-connected system voltage; L is the filter inductor; U g is the stable value of the grid-side voltage; ω N is the synchronous angular velocity;

[0011] S1.2. Obtain the VSG control parameters and the system network operation parameters in the stable state, and taking the dq rotating coordinate system as the reference system, the expression of the output impedance of the grid-side converter based on VSG is obtained as:

[0012]

[0013] where, [Δu sd , Δu sq T is the stator-side voltage disturbance vector of the grid-connected system; [Δi sd , Δi sq T is the stator-side current response vector of the grid-connected system; Z out is the output impedance of the grid-side converter based on VSG; Z dd , Z dq , Z qd and Z qq represent the d-d, d-q, q-d and q-q axis components of the output impedance Z out respectively; I represents the identity matrix.

[0014] Revealing the positive damping characteristics of the grid-side converter based on VSG to subsynchronous oscillation from the perspective of the equivalent impedance of the doubly-fed wind turbine grid-connected system includes:

[0015] S2.1. The mathematical expression of the equivalent output impedance Z G of the doubly-fed wind turbine is: ​​

[0016]

[0017] Among them, R G and X G are the equivalent resistance and reactance of the doubly-fed wind turbine respectively; R s is the sum of the resistances of the stator winding of the doubly-fed wind turbine and the transformer; R r is the resistance of the rotor winding; R RSC represents the equivalent resistance of the rotor-side converter; L ls is the sum of the leakage inductances of the stator winding of the doubly-fed wind turbine and the transformer; L lr is the rotor leakage inductance; L m is the excitation inductance; slip ratio f r and j represent the rotor frequency and the imaginary unit respectively; the resonant frequency of the inductance and capacitance series resonance circuit ω ss and f0 are the resonant frequency of the equivalent series circuit of the system under subsynchronous oscillation and the system base frequency respectively; X C 、X L are the capacitive reactance of the series capacitor and the equivalent reactance of the system respectively;

[0018] After S2.2 and the VSG are connected to the grid-side converter control of the doubly-fed wind turbine, the equivalent output impedance Z G1 of the doubly-fed wind turbine based on the VSG is obtained, and the expression is:

[0019]

[0020] Among them, R VSG and X VSG are the equivalent resistance and reactance of the VSG respectively; R G1 and X G1 are the equivalent resistance and reactance of the doubly-fed wind turbine after connecting the VSG respectively.

[0021] The mechanism for suppressing subsynchronous oscillation of the virtual synchronous doubly-fed wind turbine grid-connected system by combining active disturbance rejection control includes:

[0022] Taking the d-axis analysis as an example, the mathematical expression of the output voltage of the current inner loop of the grid-side converter under the connection of the VSG is:

[0023]

[0024] Among them, u gd is the d-axis component of the output voltage of the grid-side converter; R g and L g are the resistance and inductance of the grid-side incoming line reactor respectively; i gd and i gq are the d-axis and q-axis components of the grid input current respectively; ω Nis the synchronous angular velocity; E VSGd is the d-axis component of the VSG output voltage;

[0025] When the grid-connected system undergoes subsynchronous oscillation, the output voltage expression of the current inner loop of the grid-side converter under perturbation is rewritten as:

[0026]

[0027] Among them, Δu sub_gd and ΔE sub_VSGd are respectively the subsynchronous voltage output by the grid-side converter and the d-axis component of the subsynchronous voltage output by the VSG under perturbation; Δi sub_gd and Δi sub_gq are respectively the d- and q-axis components of the subsynchronous current;

[0028] Analyze the influence law of the PI control parameters of the current inner loop of the grid-side converter on subsynchronous oscillation, and obtain the mathematical expression of the output voltage of the current inner loop of the grid-side converter based on PI control as:

[0029]

[0030] Among them, K p2 and K i2 are respectively the d-axis proportional coefficient and integral coefficient of the PI controller in the current inner loop control of the grid-side converter; s is the Laplace operator;

[0031] When the grid-connected system operates stably, the d-axis current expression of the grid-side converter under VSG control is obtained as:

[0032]

[0033] When there are subsynchronous oscillation components in the system, the subsynchronous oscillation flows through the control link of the grid-side converter in the form of subsynchronous current and voltage components, resulting in the d-axis current of the grid-side converter becoming:

[0034]

[0035] The equation transformation is as follows:

[0036]

[0037] Among them, f1(Δi sub_gd ,Δi sub_gq ) is the d-axis component of the subsynchronous current in the grid-connected system;

[0038] Before and after adopting the active disturbance rejection controller, the d-axis current mathematical expression of the grid-side converter is obtained as:

[0039]

[0040] The q-axis is the same by the same token.

[0041] The constructed active disturbance rejection controller is improved and includes:

[0042] S4.1. To suppress the subsynchronous oscillation of the doubly-fed wind turbine grid-connected system under VSG control, replace the PI controller in the current inner loop of the grid-side converter with the active disturbance rejection controller. Then, the mathematical expression of the grid-side converter current is rewritten as:

[0043]

[0044] where, i gd and i gq are the d-axis and q-axis components of the grid input current respectively; u gd and u gq are the d-axis and q-axis components of the grid-side converter output voltage respectively; b d and b q are the d-axis and q-axis components of the dynamic compensation factor respectively; f1(Δi sub_gd ,Δi sub_gq ) is the d-axis component of the subsynchronous current in the grid-connected system; f2(Δi sub_gd ,Δi sub_gq ) represents the q-axis component of the subsynchronous current in the grid-connected system; R g and L g are the resistance and inductance of the grid-side incoming line reactor respectively; ω N is the synchronous angular velocity; E VSGd is the d-axis component of the VSG output voltage;

[0045] It can be seen that there is coupling between the d-axis and q-axis of the current inner loop control of the grid-side converter. To achieve precise decoupling control of the grid-side converter output current, include the coupling term in the disturbance, then it becomes:

[0046]

[0047] where, F1(Δi sub_gd ,Δi sub_gq ) and F2(Δi sub_gd ,Δi sub_gq ) are the d-axis component and q-axis component of the total amount of the subsynchronous disturbance and coupling amount controlled by the grid-side converter respectively;

[0048] S4.2. Construction of the improved active disturbance rejection controller, including: an extended state observer, a linear error feedback LSEF;

[0049] S4.3. Performance analysis of the improved active disturbance rejection controller.

[0050] The extended state observer ESO is to place the Fal function filter after the output of the virtual synchronous doubly-fed wind turbine connected to the grid through series compensation, and together with the traditional extended state observer ESO, form an extended state observer.

[0051] It also includes a verification step: verifying the suppression effect of the proposed improved active disturbance rejection controller strategy on sub-synchronous oscillation under different disturbance conditions.

[0052] The different disturbance conditions include: different numbers of wind turbines, wind farm wind speed, series compensation degree, and grounding fault types.

[0053] According to another aspect of the present invention, there is also provided a sub-synchronous oscillation suppression system for a virtual synchronous doubly-fed wind turbine connected to the grid through series compensation, including: a first construction module for placing the Fal function filter after the output of the virtual synchronous doubly-fed wind turbine connected to the grid through series compensation, and together with the traditional extended state observer ESO, constructing an extended state observer; a second construction module for constructing an improved active disturbance rejection controller based on the extended state observer and the linear error feedback LSEF; a suppression module for suppressing the sub-synchronous oscillation of the virtual synchronous doubly-fed wind turbine connected to the grid through series compensation by using the improved active disturbance rejection controller.

[0054] It also includes: a verification module for verifying the suppression effect of the proposed improved active disturbance rejection controller strategy on sub-synchronous oscillation under different disturbance conditions.

[0055] The beneficial effects of the present invention are as follows: The present invention reveals the influence mechanism of VSG on sub-synchronous oscillation from the equivalent impedance of the doubly-fed wind turbine grid-connected system. Based on the traditional analysis of sub-synchronous oscillation mechanism, this method focuses on analyzing the action law of the VSG output impedance on the system equivalent impedance, which has strong reference and reference significance for the sub-synchronous oscillation problems of VSG applied to direct-drive wind turbines and weak flexible DC power grids, and has strong expansibility and extensibility. Aiming at the problem that VSG cannot provide sufficient positive damping for the system, the present invention deduces the sub-synchronous oscillation suppression mechanism of the virtual synchronous doubly-fed wind turbine grid-connected system combined with active disturbance rejection control. This analysis method has the advantages of clear physical meaning and clear derivation process; in addition, the sub-synchronous oscillation suppression strategy proposed by the present invention has strong robustness to different disturbance conditions such as different series compensation degrees, wind speeds, numbers of wind turbines, and grounding short-circuit faults, and can provide a certain theoretical analysis basis for the active application of VSG in the doubly-fed wind turbine grid-connected system. To sum up, the sub-synchronous oscillation analysis method adopted by the present invention has a certain universality and can provide a theoretical analysis basis for the sub-synchronous oscillation problems brought by high-proportion power electronic devices participating in the new energy power generation system. At the same time, the suppression method proposed by the present invention is not only applicable to doubly-fed generating units, but also applicable to the suppression of sub-synchronous oscillation in direct-drive wind turbines and weak AC systems. Description of the Drawings

[0056] Figure 1 This is the main circuit topology diagram of the virtual synchronous doubly-fed wind turbine grid-connected system in an embodiment of the present invention;

[0057] Figure 2 This is the small-signal output impedance model of the converter under VSG control in an embodiment of the present invention;

[0058] Figure 3 This is the small-signal equivalent circuit diagram of the converter in the dq rotating coordinate system in an embodiment of the present invention;

[0059] Figure 4 This is the Bode diagram of the output impedance of the grid-side converter under VSG control in an embodiment of the present invention;

[0060] Figure 5 This is the structure diagram of the first-order active disturbance rejection controller in an embodiment of the present invention;

[0061] Figure 6 This is the topology structure diagram of the Fal function filter in an embodiment of the present invention;

[0062] Figure 7 This is the suppression strategy of the grid-side converter of the doubly-fed wind turbine based on active disturbance rejection control in an embodiment of the present invention;

[0063] Figure 8 This is the test model of the doubly-fed wind turbine grid-connected system with series compensation based on VSG control in an embodiment of the present invention;

[0064] Figure 9 This is the comparison diagram of the active output and current FFT analysis of the system before and after the access of VSG in an embodiment of the present invention; among them, (a) is the active power output of the wind farm under different series compensation degrees before and after the access of VSG, and (b) is the FFT analysis diagram of the current in the wind farm under different series compensation degrees before and after the access of VSG;

[0065] Figure 10 This is the comparison diagram of the response characteristic curves of the PI controller and the active disturbance rejection controller under 0.4 series compensation degree in an embodiment of the present invention; among them, (a) is the waveform diagram of the active power output of the wind farm under different controls, (b) is the waveform diagram of the reactive power output of the wind farm under different controls, and (c) is the waveform diagram of the phase A current on the 690V side of the wind farm under different controls;

[0066] Figure 11 This is the comparison diagram of the response characteristic curves of the PI controller and the active disturbance rejection controller under 0.6 series compensation degree in an embodiment of the present invention; among them, (a) is the waveform diagram of the active power output of the wind farm under different controls, (b) is the waveform diagram of the reactive power output of the wind farm under different controls, and (c) is the waveform diagram of the phase A current on the 690V side of the wind farm under different controls;

[0067] Figure 12Active power response curves under different measures when the number of wind turbines changes in an embodiment of the present invention; among them, (a) is the active power output of the wind farm under different controls when there are 80 wind turbines, (b) is the active power output of the wind farm under different controls when there are 67 wind turbines, and (c) is the active power output of the wind farm under different controls when there are 50 wind turbines;

[0068] Figure 13 Active power response curves under different suppression measures when the wind speed changes in an embodiment of the present invention; among them, (a) is the active power output of the wind farm under different controls when the wind speed is 11 m / s, (b) is the active power output of the wind farm under different controls when the wind speed is 10 m / s, and (c) is the active power output of the wind farm under different controls when the wind speed is 9 m / s;

[0069] Figure 14 Active power response curves under different suppression measures for different grounding short - circuit faults in an embodiment of the present invention; among them, (a) is the active power output of the wind farm under different controls for single - phase grounding short - circuit faults, (b) is the active power output of the wind farm under different controls for two - phase grounding short - circuit faults, and (c) is the active power output of the wind farm under different controls for three - phase grounding short - circuit faults. Detailed implementation manners

[0070] The following will further illustrate the invention in conjunction with the drawings and embodiments, but the content of the present invention is not limited to the described scope.

[0071] Embodiment 1: As Figure 1-14 shown, a method for suppressing subsynchronous oscillation of a virtual - synchronous doubly - fed wind turbine connected to the grid through series compensation includes: obtaining the output impedance expression of the grid - side converter based on VSG; revealing the positive damping characteristics of the grid - side converter based on VSG for subsynchronous oscillation from the perspective of the equivalent impedance of the doubly - fed wind turbine grid - connected system; analyzing the mechanism of suppressing subsynchronous oscillation of the virtual - synchronous doubly - fed wind turbine grid - connected system in combination with active disturbance rejection control; and constructing an improved active disturbance rejection controller to suppress subsynchronous oscillation.

[0072] Furthermore, an optional implementation process of the present invention will be described below:

[0073] The present invention selects as Figure 1The topological structure of the virtual synchronous doubly-fed wind turbine grid-connected system shown is implemented as a case. In the embodiment of the present invention, it includes a doubly-fed wind power generation set, a rotor-side converter (rotor-side inverter), a grid-side converter (grid-side inverter), a DC filter capacitor, a VSG controller, a phase-locked loop, and a series compensation network. Based on the conventional double-loop control strategy, voltage feedforward control is added to the grid-side converter to achieve virtual synchronous control of the doubly-fed wind turbine. The specific process is that the output voltage of the VSG control is connected to the current inner-loop control of the grid-side converter of the doubly-fed wind turbine and used as a feedforward signal for feedforward control. The DC filter capacitor between the rotor-side converter and the grid-side converter constitutes a DC link, and the LCL filter of the grid-side converter is connected to the power grid as the output end.

[0074] The derivation and analysis process of the present invention will be further described in detail below with reference to the accompanying drawings.

[0075] Specifically, the operating parameters and control parameters in this example can be expressed as follows:

[0076] Table 1 Parameters of a single doubly-fed wind turbine

[0077] Parameter Value and Unit Rated Power 1.5MW Rated Frequency 50Hz Rated Stator Voltage 690V <![CDATA[Stator resistance R s > 0.023p.u. <![CDATA[Stator leakage inductance L ls > 0.018p.u. <![CDATA[Rotor resistance R r > 0.016p.u. <![CDATA[Rotor leakage inductance L lr > 0.16p.u. <![CDATA[Excitation inductance L m > 2.9p.u. <![CDATA[DC voltage U dc > 1.15kV <![CDATA[0.69 / 35kV On-site Transformer X T1 > 0.06 <![CDATA[0.69 / 35kV In-field Transformer R T1 > 0.015

[0078] Table 2 Parameters of the doubly-fed wind turbine controller

[0079]

[0080] Table 3 Parameters of the transformer and line

[0081] Parameter Value and Unit Parameter Value and Unit <![CDATA[220 kV line resistance R L1 > 0.01p.u. <![CDATA[35 / 200 kV transformer reactance X T2 > 0.06p.u. <![CDATA[Reactance X of 220 kV line L1 > 0.1p.u. <![CDATA[220 / 500kV transformer reactance X T3 > 0.14.p.u <![CDATA[500kV line resistance R L2 > 0.005p.u. <![CDATA[Series compensation capacitor C at 0.4 series compensation degree L2 > (0.0962e-03)F <![CDATA[500kV line reactance X L2 > 0.033p.u.

[0082] Note: The basic capacity is 100 MW

[0083] See Figure 2-14 , a method and control system for suppressing subsynchronous oscillation of a virtual synchronous doubly-fed wind turbine connected to the grid through series compensation provided by the present invention, the specific steps are as follows:

[0084] Step S1: Based on the small-signal model of the virtual synchronous generator VSG, derive the expression of the output impedance of the grid-side converter based on VSG;

[0085] Step S2: From the perspective of the equivalent impedance of the doubly-fed wind turbine grid-connected system, reveal the positive damping characteristic of VSG for subsynchronous oscillation;

[0086] Step S3: In view of the fact that the output impedance of VSG is small and cannot effectively suppress subsynchronous oscillation, derive the suppression mechanism of subsynchronous oscillation combined with active disturbance rejection control;

[0087] Step S4: Design a Fal function filter to improve and optimize the output voltage waveform, and construct each part of the active disturbance rejection control in detail, and then discuss the stability of the designed controller;

[0088] Step S5: Compare and analyze the traditional PI control, and verify the adaptability of the proposed strategy to sub-synchronous oscillation under different disturbance conditions.

[0089] The specific content of the said step S1 is as follows:

[0090] S1.1: Adopt the small-signal stability analysis method of the power system, and linearize the dynamic equation of the VSG based on the control topology of the VSG. The control principle of the VSG can be expressed as: The VSG simulates the moment of inertia, primary frequency regulation characteristics and voltage regulation characteristics in the synchronous generator, and provides necessary voltage and frequency support for the power grid. Different from the synchronous generator, the VSG can independently design the active power and reactive power input according to the power grid frequency and voltage, and has good grid connection performance, mainly including three parts: active loop control, excitation control and output voltage control. The mathematical expressions of the active loop control and the excitation control can be expressed as:

[0091]

[0092] where, T J and D p are the moment of inertia and the damping coefficient respectively; K f and K v are the droop coefficients of the active power-frequency control and the reactive power-voltage control respectively; P ref and P set are the reference value and the set value of the droop control active power respectively; f N and f v are the reference frequency and the synchronous frequency of the grid-connected system respectively; u rms and u N are the root mean square value of the grid-side voltage and the rated voltage of the grid-connected system respectively; ω N and ω v are the reference angular frequency of the grid-connected system and the output angular frequency of the VSG respectively; K p and K i are the proportional coefficient and the integral coefficient of the excitation control respectively; Q set and u ref are the set value of the reactive power of the grid-connected system and the voltage reference value of the reactive power-voltage control respectively; λ1 is the proportional coefficient of the VSG output phase angle; θ m and E m are the active control output phase angle of the VSG and the excitation control output voltage respectively.

[0093] The input active power P m and reactive power Q m of the VSG control can be expressed by the power equation as:

[0094]

[0095] Among them, u d , u q are the dq-axis components of the grid voltage respectively; i d , i q are the dq-axis components of the grid-side current respectively.

[0096] The three-phase voltage e mi (i = a, b, c) output by the VSG is determined jointly by the active loop control output θ m and the excitation control output E m , and can be realized through the synchronization equation. Its mathematical expression is:

[0097]

[0098] When a small disturbance is applied and local linearization is performed when the VSG is stable, the small-signal output impedance model of the grid-side converter under VSG control can be obtained, as shown in Figure 2 .

[0099] Furthermore, in the small-signal model shown in Figure 2 , F PQ , F PI , F1, F L , F2 are all expressed as 2×2 order transfer function matrices. Among them:

[0100]

[0101] Among them, F PQ , F PI , F1, F L , F2 are 2×2 order transfer function matrices; F PQ is the transfer function matrix from the power vector to the vector [Δθ m , ΔE m T ; F PI is the PI control transfer function matrix; F1 is the transfer function matrix from the vector [Δθ m , ΔE m T to the vector [ΔE d , ΔE q T ; F L is the transfer function matrix from the vector [ΔE VSGd , ΔE VSGq T to the current response vector [Δi sd , Δi sq T ; and ​​​​​is the small-signal transfer function matrix for power calculation; F2 is the voltage perturbation vector [Δu sd , Δu sq T to the transfer function matrix of [ΔE d , ΔE q T . T J and D p are the moment of inertia and damping coefficient respectively; K p and K i are the excitation control proportional coefficient and integral coefficient respectively; Q set and u ref are the reactive power set value of the grid-connected system and the reactive power-voltage control voltage reference value respectively; θ m and E m are the phase angle of the active power control output of VSG and the excitation control output voltage respectively; K Vp1 and K Vi1 are the d-axis proportional coefficient and integral coefficient of the VSG output voltage control respectively; K Vp2 and K Vi2 are the q-axis proportional coefficient and integral coefficient of the VSG output voltage control respectively; U sd and U sq are the steady-state operating points of the stator voltage in the synchronous rotating coordinate system; I sd and I sq are the steady-state operating points of the stator current in the synchronous rotating coordinate system; L is the filter inductor; δ is the difference between the phase angle output by the phase-locked loop and the phase of the grid-connected system voltage; U g is the grid-side voltage stability value; s is the Laplace operator; ω N is the synchronous angular velocity.

[0102] S1.2. Since the active power P ref and reactive power Q ref command signals remain unchanged during the entire control process, the power command perturbation term can be considered 0, and at the same time, it is assumed that the DC bus voltage is constant. Obtain the control and operation parameters when VSG is stable, as shown in Table 1 - Table 2. Taking the dq rotating coordinate as the reference system and combining with the small-signal circuit of the converter Figure 3 the output impedance expression of the grid-side converter can be obtained as:

[0103]

[0104] where, [Δu sd , Δu sq T is defined as the voltage perturbation amount on the stator side of the grid-connected system; [Δi sd , Δi sq T is the grid-connected system stator side current response vector; Z​​​​out is the output impedance of the grid-side converter; Z dd , Z dq , Z qd and Z qq respectively represent the d-d, d-q, q-d, and q-q axis components of the output impedance Z out .

[0105] Furthermore, the output impedance expression of the grid-side converter based on VSG is derived as follows:

[0106]

[0107] where I represents the identity matrix.

[0108] Taking a VSG with a rated power of 1500 kW as an example, the frequency characteristics of its output impedance are analyzed. The rated active power P of this VSG is 1500 kW, the rated reactive power Q is 0 kvar, the switching frequency is 10 kHz, the filtering inductor L is 4.5 mH, and the remaining control parameters are shown in Tables 1 - 2 specifically. The Bode diagram of the output impedance of the grid-side converter under VSG control can be obtained, as shown in Figure 4 .

[0109] Based on Figure 4 , it can be known that the output impedance of the grid-connected converter based on VSG control is positive at the base frequency, showing a weak impedance characteristic. Analyzing the magnitude relationship of the output impedance of the grid-side converter under VSG control in the dq axis direction, it can be considered that Z dd and the equivalent impedance Z qd of the q axis with respect to the d axis have approximately equal amplitudes, and Z qq and the equivalent impedance Z dq of the d axis with respect to the q axis have approximately equal amplitudes. By superimposing the corresponding impedance values on the dq axes respectively, dq approximate decoupling can be achieved. Further analyzing from the perspective of the synchronous resistance and reactance characteristics of the synchronous generator, the output impedance of the grid-side converter under VSG control can be expressed as Z VSG = R VSG + jX VSG .

[0110] The specific steps of step S2 are as follows:

[0111] S2.1. Derivation of the equivalent impedance of the doubly-fed wind turbine grid-connected system. In the doubly-fed wind turbine grid-connected system, the capacitive reactance of the series capacitor and the inductive reactance of the system are connected in series to form an inductance and capacitance series resonance circuit. Based on existing literature, there is a direct corresponding relationship between the occurrence of subsynchronous oscillation and the magnitude of the equivalent impedance of the doubly-fed wind turbine. Among them, the mathematical expression of the equivalent impedance Z G of the doubly-fed wind turbine under subsynchronous oscillation can be expressed as:

[0112]

[0113] Among them, R G and X G are the equivalent resistance and reactance of the doubly-fed wind turbine respectively; R s is the sum of the stator winding resistance of the doubly-fed wind turbine and the transformer resistance; R r is the resistance of the rotor winding; R RSC represents the equivalent resistance of the rotor-side converter; X ls is the sum of the leakage inductance of the stator winding of the doubly-fed wind turbine and the transformer resistance leakage inductance; X lr is the rotor leakage reactance; X m is the excitation inductance; slip ratio f r is the rotor frequency; the resonance frequency of the inductance and capacitance series resonance circuit j represents the imaginary unit; Z G is the equivalent output impedance expression of the doubly-fed wind turbine; ω ss and f0 are the resonance frequency of the equivalent series circuit of the system under subsynchronous oscillation and the system base frequency respectively; X C and X L are the capacitive reactance of the series compensation capacitor and the equivalent reactance of the system respectively.

[0114] It can be seen that the magnitude of the output impedance of the doubly-fed wind turbine is affected by the slip ratio and the equivalent resistance of the rotor-side converter. Since the slip ratio is negative, when the rotor resistance and the equivalent resistance of the rotor-side converter are greater than the sum of the other resistance vectors, the equivalent resistance of the system exhibits a negative resistance characteristic, causing the inductance and capacitance resonance circuit to oscillate continuously and diverge, resulting in subsynchronous oscillation.

[0115] S2.2. After the VSG is connected to the grid-side converter control of the doubly-fed wind turbine, the equivalent output impedance expression of the doubly-fed wind turbine based on the VSG is obtained as:

[0116]

[0117] Among them, R VSG and X VSG are the equivalent resistance and reactance of the VSG respectively; R G1 and X G1 are the equivalent resistance and reactance of the doubly-fed wind turbine after connecting the VSG respectively; Z G1 is the equivalent output impedance of the doubly-fed wind turbine based on VSG control.

[0118] It can be seen that the access of the VSG can reduce the degree of negative impedance of the system, making the virtual synchronous control method of the doubly-fed wind turbine based on the grid-side converter VSG have an inhibitory effect on subsynchronous oscillation. However, due to the small output impedance value of the grid-side converter under VSG control, there is an obvious phenomenon of insufficient inhibitory ability, and the positive and negative of the equivalent resistance of the system more depends on the equivalent resistance of the rotor-side converter and the line resistance. Therefore, the VSG cannot completely suppress the occurrence of subsynchronous oscillation, but only weaken the action intensity of subsynchronous oscillation to a certain extent.

[0119] The specific steps of step S3 are as follows:

[0120] Due to the small output impedance of the VSG, there is a risk of subsynchronous oscillation in the grid-connected system of the doubly-fed wind turbine under the VSG control method of the grid-side converter. Therefore, the mechanism of suppressing subsynchronous oscillation under VSG control is explored in combination with the active disturbance rejection control. The active disturbance rejection control can expand the internal and external disturbances and uncertain factors of the system into the system state variables to perform real-time feedback and compensation on the system controller, thereby realizing the effective suppression of the disturbance. The structure diagram of the active disturbance rejection control is as Figure 5 shown. Among them, v0 is the reference value of the controlled quantity; y is the output value of the controlled quantity; z1 is the tracking signal of the output y; z2 is the observed value of the total disturbance; f0 is the known part of the system; u is the final control quantity of the system; b0 is the dynamic compensation factor.

[0121] To simplify the analysis process, taking the d-axis analysis as an example. Then the mathematical expression of the output voltage of the current inner loop of the grid-side converter under the access of VSG control can be expressed as:

[0122]

[0123] Among them, u gd is the d-axis component of the output voltage of the grid-side converter; R g and L g are the resistance and inductance of the grid-side incoming line reactor respectively; i gd and i gq are the d-axis and q-axis components of the grid input current respectively; ω N is the synchronous angular velocity; E VSGd is the d-axis component of the VSG output voltage.

[0124] When the grid-connected system has a subsynchronous oscillation, the expression of the output voltage of the current inner loop of the grid-side converter under the disturbance can be rewritten as:

[0125]

[0126] Among them, Δu sub_gd and ΔE sub_VSGd are the d-axis components of the subsynchronous voltage output by the grid-side converter and the subsynchronous voltage output by the VSG under the disturbance respectively; Δi sub_gd and Δi sub_gqThey are the d-axis and q-axis components of the subsynchronous current respectively.

[0127] Further analyze the influence law of the current inner-loop PI control parameters of the grid-side converter on subsynchronous oscillation. Since the differential link is often equivalently replaced by a PI controller in engineering practice, good control effects can also be obtained. Based on this, the mathematical expression of the output voltage of the current inner-loop of the grid-side converter based on PI control is obtained as follows:

[0128]

[0129] It can be seen that the subsynchronous oscillation component passes through the current inner-loop PI control link of the grid-side converter in the form of current, and then a subsynchronous component is superimposed on the grid-side output voltage, making the control part of the grid-side converter with VSG all carry the subsynchronous component. At the same time, due to the proportional link in the PI controller, the subsynchronous oscillation amount is further amplified, resulting in intensified oscillation.

[0130] In addition, since wind farms often cause the system operation to be variable due to factors such as the number of wind turbines, wind speed, and grounding faults, it is difficult to effectively suppress subsynchronous oscillation by adjusting the PI control parameters. From the above analysis, if the output current of the grid-side converter is kept stable under subsynchronous oscillation, the subsynchronous oscillation component in the grid-side converter output voltage can be eliminated, thereby destroying the action path of subsynchronous oscillation and achieving the purpose of suppressing subsynchronous oscillation.

[0131] Therefore, it is proposed to use active disturbance rejection control to replace PI control to estimate and compensate the influence of subsynchronous current on the output current of the wind turbine in real time, so as to achieve the stability of the grid-side output voltage and the suppression of subsynchronous oscillation. The suppression principle is specifically expressed as:

[0132] When the grid-connected system operates stably, the expression of the d-axis current of the grid-side converter under VSG control can be obtained as:

[0133]

[0134] When there is a subsynchronous oscillation component in the system, the subsynchronous oscillation flows through the control link of the grid-side converter in the form of subsynchronous current and voltage components, resulting in the d-axis current of the grid-side converter becoming:

[0135]

[0136] To clearly analyze the overall influence of the subsynchronous oscillation component on the voltage and current of the grid-side converter, the following equation transformation is made:

[0137]

[0138] Among them, f1(Δi sub_gd , Δi sub_gq ) can represent the d-axis component of the subsynchronous current in the grid-connected system.

[0139] It can be seen that the disturbance effect of the subsynchronous oscillation on the grid-side converter can be expressed by f1(Δi sub_gd ,Δi sub_gq ). If this disturbance term is eliminated, the subsynchronous oscillation will be suppressed. For this reason, since the active disturbance rejection controller can estimate f1(Δi sub_d ,Δi sub_q ) in real time and perform real-time compensation on the output voltage of the grid-side converter. Then, before and after the active disturbance rejection controller is adopted, the mathematical expressions of the d-axis current of the grid-side converter are as follows:

[0140]

[0141] In the formula, the above formula is before the active disturbance rejection controller is adopted, and the following formula is after the active disturbance rejection controller is adopted; through comparative analysis, it can be found that the output current i gd of the grid-side converter under subsynchronous oscillation is consistent with the expression during the stable operation of the system. It can be considered that under the active disturbance rejection controller, i gd is not affected by the subsynchronous current component Δi sub_d , blocking the transmission process of the subsynchronous voltage component Δu gd in the output voltage u sub_d of the grid-side converter, and thus achieving the purpose of suppressing the subsynchronous oscillation.

[0142] The specific steps of step S4 are as follows:

[0143] S4.1. To suppress the subsynchronous oscillation of the system under VSG control, this paper replaces the current inner-loop PI controller of the grid-side converter with an active disturbance rejection control. The current of the grid-side converter can be expressed as:

[0144]

[0145] Among them, i gd and i gq are the d-axis and q-axis components of the grid input current respectively; u gd and u gq are the d-axis and q-axis components of the output voltage of the grid-side converter respectively; b d and b q are the d-axis and q-axis components of the dynamic compensation factor respectively; f1(Δi sub_gd ,Δi sub_gq ) is the d-axis component of the subsynchronous current in the grid-connected system; f2(Δi sub_gd ,Δi sub_gq ) represents the q-axis component of the subsynchronous current in the grid-connected system; R g and L g are the resistance and inductance of the grid-side incoming line reactor respectively; ω N is the synchronous angular velocity; E VSGdis the d-axis component of the VSG output voltage.

[0146] It can be seen that there is coupling between the d-axis and q-axis of the inner current loop control of the grid-side converter. To achieve precise decoupling control of the current, the coupling term is included in the disturbance, and it can be changed to:

[0147]

[0148] where F1(Δi sub_gd , Δi sub_gq ) and F2(Δi sub_gd , Δi sub_gq ) are the sub-synchronous disturbances and coupling quantities of the d-axis and q-axis control of the grid-side converter respectively.

[0149] S4.2. Construction of the improved active disturbance rejection control, including: non-linear differential tracker (TD), extended state observer (ESO), and linear error feedback (LSEF), is as follows:

[0150] 1) Since the tracking differential link of the first-order active disturbance rejection controller only outputs the tracking signal and does not output the differential signal, the non-linear tracking differentiator link can be omitted.

[0151] 2) Extended type extended state observer link with filtering effect

[0152] The extended state observer (ESO) can track the state information and estimate the system disturbance according to the system output and the input of the controlled object, so as to generate the disturbance compensation amount. Among them, the Fal function is the core component unit of the ESO, showing the correction characteristics of "large error, small gain; small error, large gain".

[0153] In addition, at present, the ESO rarely considers the noise interference existing in the system output measurement link, which is common in actual control. The large gain coefficient in the ESO will amplify the measurement noise, which has a great impact on the performance of the observer. Generally, in the actual control loop, a filter is used to process the system output to filter the noise interference, but there are large differences in the amplitude and phase of the filtered signal and the true output of the system. If this is used as the system output to construct the observer, it will inevitably cause large observation errors. Therefore, an improved form of constructing the extended state observer is adopted, and the Fal function filter is placed after the system output to improve the output waveform quality and form an extended ESO together with the ESO. It not only retains the original advantages and maintains the state order, but also can effectively process the noise introduced by the measurement link.

[0154] The control structure of the Fal function filter is as Figure 6 shown. Among them, k Fal is the proportional coefficient; α f is a constant between 0 and 1; δf is a constant affecting the filtering effect; U is the input signal; Y is the output signal of U passing through the control structure of the Fal function filter. When the error e is less than δ f let k1 = k Fal / δ f 1-αf , then the transfer function expression of the output Fal function feedback structure can be obtained as:

[0155]

[0156] It can be seen that the transfer function expression of the output Fal function feedback structure is actually a low-pass filter. When δ f increases or k Fal decreases, that is, k1 decreases, the filter bandwidth becomes narrower and the tracking speed becomes slower, and a better filtering effect can be obtained.

[0157] In summary, by expanding the observed disturbance term of the system into a new state variable, an extended extended state observer can be obtained, and its mathematical expression is:

[0158]

[0159] where β 01 , β 02 are gain coefficients; F d is the total disturbance of the d-axis of the system (including the unmodeled part of the system more than F1); i gd and are the instantaneous value and estimated value of the d-axis component of the grid-side power grid respectively; e d is the difference between the estimated value and the instantaneous value of the d-axis component of the grid-side power grid; is the observed value of the d-axis disturbance; is the output value after the d-axis component of the grid-side voltage passes through the fal function filtering structure.

[0160] 3) Linear state error feedback (LSEF) link

[0161] Since it is difficult to select the control parameters of the nonlinear state error feedback link, and to simplify the controller design process, linear state error feedback is mostly used instead, which can also achieve better suppression of disturbances. Combining the ESO estimation of the comprehensive disturbance, real-time disturbance compensation is performed on the feedback control quantity, so as to achieve the purpose of suppressing oscillations. Therefore, based on the established extended state observer, according to the design principle of linear state error feedback control, the error feedback form can be obtained as:

[0162]

[0163] where e Nd is the reference value of the d-axis current of the grid-side converter i gdrefThe signal difference between the estimated value of i output by the ESO; u gd is the output of the improved active disturbance rejection controller without ESO dynamic compensation; k is an adjustable coefficient. 0d For the output of the improved active disturbance rejection controller without ESO dynamic compensation; k is an adjustable coefficient.

[0164] Furthermore, the combined disturbance estimated by the ESO can perform real-time disturbance compensation on the feedback control quantity, so as to achieve the purpose of suppressing oscillation. The final control quantity formed by the disturbance estimation compensation is:[[]]

[0165]

[0166] It should be noted that due to the strong dependence of the closed-loop nature of the active disturbance rejection control on the control parameters, the control parameters can achieve good robustness and adaptability through simple tuning. Among them, the simulation sampling step size h is a basic parameter, and the gain parameters β 01 and β 02 are selected to be directly related to h. In this paper, β 01 = 1 / h, β 02 =(β 01 ) 3 ; the dynamic participation factor b x is the estimated value of the amplification coefficient when the control quantity acts on the system, and only needs to be slightly adjusted; the parameter k of the linear state feedback link is an adjustable coefficient, and the smaller its value, the better the control effect. Therefore, the appropriate value of k can be selected according to the simulation effect.

[0167] In summary, based on the combined disturbance estimated by the ESO, real-time disturbance compensation is performed on the feedback control quantity, and an active disturbance rejection controller is designed to replace the PI control link of the grid-side converter current inner loop. On the basis of ensuring the stability of the VSG control performance, with the goal of eliminating the subsynchronous current and voltage components, effective suppression of subsynchronous oscillation can be achieved. The control strategy proposed in the present invention is as Figure 7 shown.

[0168] S5.3. Controller performance analysis. Since the d and q axes have the same expression form, only the d axis is taken as an example to analyze three parts: the stability of the ESO, the observation error of the ESO, and the stability of the closed-loop system.

[0169] 1) ESO stability analysis

[0170] To simplify the calculation process, let:

[0171]

[0172] Select α1 = α2, δ1 = δ2, then there is:

[0173] ρ1(e d ) = ρ2(e d ) = ρ(e d )

[0174] Thus, by expanding the disturbance term of the observed system into a new state variable, a simplified extended state observer can be obtained, and its expression becomes:

[0175]

[0176] The above equation can be equivalent to a variable coefficient linear system and re-expressed in matrix form, and its expression is:

[0177]

[0178] Furthermore, through Laplace transform, the ESO transfer function expression can be calculated as:

[0179]

[0180] For the above equation, it can be regarded as a variable coefficient linear system with perturbations within a finite range of parameters, and its stability can be analyzed using the root locus method. It can be seen that the characteristic equation of the system can be expressed as: s 2 +β 01 ρ(e d )s + β 02 ρ(e d ) = 0. List the Routh table as shown in Table 4:

[0181] Table 4

[0182] <![CDATA[s 2 > 1 <![CDATA[β 02 ρ(e d )]]> <![CDATA[s 1 > <![CDATA[β 01 ρ(e d )]]> <![CDATA[s 0 > <![CDATA[β 02 ρ(e d )]]>

[0183] According to the Routh criterion, the system stability condition is:

[0184]

[0185] Since the control parameters β 01 , β 02 of the present invention are both greater than 0, and α1 = α2 = 0.5, δ1 = δ2 = 0.2 are selected, it can be seen that ρ(e d ) > 0 (e d ≠0), and thus it is obtained that the designed ESO meets the stability requirements.

[0186] 2) ESO Observation Error Analysis

[0187] Based on the above analysis, by taking the total disturbance term as the system extended state variable, the expression of the state space model of the grid-side converter control output current is:

[0188]

[0189] Based on the above analysis, the ESO observation error analysis can be realized, and the mathematical expression of the error equation is:

[0190]

[0191] When the error system enters the steady state, the right side of this equation converges to zero, that is:

[0192]

[0193] Since, at this time, it can approximately satisfy Fal(e d1 , 0.5, 0.2) = |e d1 |0.5 * sign(e d1 ), therefore, the steady-state error is:

[0194]

[0195] Obviously, if β 02 is large enough compared to w d , the ESO estimation error will be small enough to meet the observation accuracy requirements.

[0196] 3) Stability analysis of the grid-side converter closed-loop control system

[0197] Due to the filtering characteristics of the Fal function feedback structure optimizing the waveform quality of the d-axis voltage , the expression of the filtered voltage u gd can be obtained as:

[0198]

[0199] Based on Figure 5 the shown control topology structure relationship, the mathematical expression of the d-axis closed-loop control system of the grid-side converter can be obtained as:

[0200]

[0201] Combining the above equations, the d-axis closed-loop transfer function of the grid-side converter can be obtained as:

[0202]

[0203] In the formula: ρ = ρ(e d ), Δ = k1s 3 +(kb d β 01 ρ + β 02 ρ + k1β 01 ρ)s 2 +(kk1b d β 01 ρ + kb d β 02 ρ + 2k1β 02 ρ)s + kk1b d β 02ρ。

[0204] From this analysis, the characteristic equation of the closed-loop system with the grid-side converter as the analysis object can be expressed as:

[0205] k1s 3 +(kb d β 01 ρ + β 02 ρ + k1β 01 ρ)s 2 +(kk1b d β 01 ρ + kb d β 02 ρ + 2k1β 02 ρ)s + kk1b d β 02 ρ = 0. List the Routh table as shown in Table 5:

[0206] Table 5

[0207] <![CDATA[s 3 > <![CDATA[k1]]> <![CDATA[kk1b d β 01 ρ+kb d β 02 ρ+2k1β 02 ρ]]> <![CDATA[s 2 > <![CDATA[kb d β 01 ρ + β 02 ρ + k1β 01 ρ]]> <![CDATA[kk1b d β 02 ρ]]> <![CDATA[s 1 > <![CDATA[b1]]> <![CDATA[s 0 > <![CDATA[kk1b d β 02 ρ]]>

[0208] where, b1 = kk1b d β 01 ρ + kb d β 02 ρ + 2k1β 02 ρ - kk1 2 b d β 02 ρ / (kb d β 01 ρ + β 02 ρ + k1β 01 ρ).

[0209] According to the Routh criterion, the system stability condition is:

[0210]

[0211] In the present invention, it is required that the control parameters β 01 、β 02 、k、k1、b d and ρ are greater than 0. Then k1 > 0, kb d β 01 ρ + β 02 ρ + k1β 01 ρ > 0 and kk1b d β 02 ρ > 0. Next, prove that b1 is greater than 0.

[0212] For the control parameters satisfying β 02 =(β 01 ) 3 ,β 02Much larger than k, k1, b d 。Based on the above analysis, |e d | < 1 can be obtained. Then, from the Fal function expression, ρ > 1 (|e d | ≠ 1, |e d | < 1). In addition, (kb d β 01 ρ + β 02 ρ + k1β 01 ρ) > β 02 ρ. According to the scaling method, (kk1 2 b d β 02 ρ / β 02 ρ) > [kk1 2 b d β 02 ρ / (kb d β 01 ρ + β 02 ρ + k1β 01 ρ)].

[0213] From this, the following relationship can be obtained:

[0214] kk1b d β 01 ρ + kb d β 02 ρ + 2k1β 02 ρ - (kk1 2 b d β 02 ρ / β 02 ρ) = kk1b d β 01 ρ + kb d β 02 ρ + 2k1β 02 ρ - kk1 2 b d > 0

[0215] Based on the above analysis, it can be proved that b1 > 0. In summary, it can be seen that the d-axis closed-loop control system of the grid-side converter meets the stability requirements. Similarly, it can be proved that the q-axis closed-loop control system also meets the stability requirements.

[0216] The specific step S5 is as follows:

[0217] Based on a wind farm in North China of China, a simulation model is built to verify the correctness of the analysis of the influence mechanism of VSG on subsynchronous oscillation and the applicability of active disturbance rejection control to subsynchronous oscillation. The simulation test model is as Figure 8As shown. The output capacity of the doubly-fed wind farm under this model is 100 MW, which consists of 67 identical 1.5 MW doubly-fed wind turbines. Each doubly-fed wind turbine is connected to the same bus via a 0.69 / 35 kV on-site transformer T1, and an aggregated wind turbine equivalent model is used to simulate the entire doubly-fed wind farm. The entire doubly-fed wind farm is connected to a 220 kV line via a 35 / 220 kV transformer T2, and finally connected to a 500 kV line via a 220 / 500 kV step-up transformer T3 for long-distance power transmission. Series capacitors are installed in the 500 kV line for compensation. In the figure, Z L1 and Z L2 are the impedances of the 220 kV and 500 kV lines respectively, and C L2 is the capacitive reactance of the series compensation capacitor. The effectiveness of the sub-synchronous oscillation analysis mechanism and the proposed suppression strategy proposed in the present invention will be verified from three aspects below. The relevant control parameters can be seen in Tables 1 - 3.

[0218] 1) Analysis and verification of the sub-synchronous oscillation mechanism of the grid-connected system before and after the VSG is connected

[0219] To verify the correctness of the influence mechanism of the VSG on the sub-synchronous oscillation of the doubly-fed wind turbine grid-connected system, keep the wind speed of the wind turbine at 11 m / s, set two series compensation degrees of 0.4 and 0.6 for the operating conditions, and obtain the FFT analysis diagrams of the active power output and the in-field current of the doubly-fed wind farm before and after the VSG is connected, as shown in Figure 9 shown.

[0220] It can be seen that after the VSG is connected, the oscillation amplitude of the active power P w output by the wind farm is reduced, and it has an inhibitory effect on sub-synchronous oscillation. Through the FFT analysis of the in-field current of the wind farm, it can be obtained that after the VSG is connected, the sub-synchronous oscillation frequency decreases, the waveform distortion rate decreases, and the sub-synchronous oscillation characteristics weaken at series compensation degrees of 0.4 and 0.6, which verifies that the virtual synchronous control of the doubly-fed wind turbine based on the grid-side converter VSG has the effect of suppressing sub-synchronous oscillation. And when the output impedance of the VSG is certain, the amplitude of the equivalent negative impedance of the system is larger at a high series compensation degree, making the inhibitory effect of the VSG on sub-synchronous oscillation better at a low series compensation degree. However, due to the small output impedance of the VSG under this control mode, it cannot provide sufficient positive damping for the system. Specifically, in Figure 9 it is shown that the degree of sub-synchronous oscillation is weakened to a certain extent after the VSG is connected, and the experimental analysis results are consistent with the theoretical analysis conclusions.

[0221] 2) Comparison of the suppression effects of the PI controller and the improved active disturbance rejection controller

[0222] To verify the effectiveness of the active disturbance rejection control in suppressing sub-synchronous oscillation, compare and analyze the abilities of the improved ADRC, the PI control, and the traditional ADRC in suppressing sub-synchronous oscillation under different series compensation degrees (where, Figure 10 and 11Among them, the improved ADRC control (i.e., the improved auto-disturbance rejection controller of the present invention). Among them, the controller parameters are set as follows: k Fal = 0.5, α f = 0.5, b d = 0.01, β 01 = 6, β 02 = 108. The simulation inputs a series compensation degree of 0.4 at 8 s, and the simulation results are as Figure 10 shown. In addition, to analyze the suppression ability of the control strategy proposed in this paper on subsynchronous oscillation under different series compensation degrees, a simulation experiment is set at a series compensation degree of 0.6, and the experimental results are as Figure 11 shown. Based on the simulation results, it can be seen that under PI control, as the series compensation capacitor is connected to the 500 KV transmission line side of the doubly-fed wind farm grid-connected system, the active power output of the fan contains a large-amplitude subsynchronous frequency component, and the current waveform distortion on the 690 V side of the field is serious, and continuous subsynchronous oscillation occurs. When the improved auto-disturbance rejection controller is adopted, with the connection of the series compensation capacitor, the active power, reactive power and current output by the wind farm only show a slight transient process at the moment of input, and then effectively and quickly eliminate the subsynchronous oscillation interference, making the system tend to be stable. Compared with the traditional auto-disturbance rejection controller, the improved auto-disturbance rejection controller combined with the Fal function filter can maintain the stability of the output current, that is, effectively weaken the influence of the interaction between the control part of the doubly-fed fan and the series compensation capacitor, and the suppression effect is better.

[0223] 3) Adaptability analysis of improved auto-disturbance rejection control

[0224] To verify the robustness of the auto-disturbance rejection control in suppressing subsynchronous oscillation, considering the characteristics of randomness and volatility of the output of the doubly-fed wind farm, the series compensation degree is set to 0.4, and the control parameters k Fal = 0.5, α f = 0.5, b d = 0.01, β 01 = 6, β 02 = 108 are maintained, and the adaptability of the auto-disturbance rejection control under different numbers of fans and wind speeds is analyzed.

[0225] (1) Change in the number of fans

[0226] The number of fans in the wind farm is changed to study the adaptability of the auto-disturbance rejection control to the change in the number of fans. The wind farm is set according to the operating conditions of 67 fans, and the simulation analysis is carried out for two operating states of increasing to 80 fans and decreasing to 50 fans. The simulation results are as Figure 12 shown (where, Figure 12Among them, ADRC control is the improved active disturbance rejection controller of the present invention. It can be seen that under the condition of three grid-connected wind turbine numbers, if the system does not take suppression measures, the active power output of the wind farm will become unstable after a fault. As the number of grid-connected wind turbines decreases, the output power of the wind farm decreases, the degree of subsynchronous oscillation intensifies, and the instability of the system increases, which means that the number of grid-connected wind turbines changes the equivalent impedance of the system, thereby affecting the damping characteristics of the system. However, after adding the active disturbance rejection control, the degree of oscillation is quickly reduced. At the initial stage of oscillation, the amplitude of the active power output of the wind farm weakens, and then the oscillation is effectively suppressed when it stabilizes, and the active power output tends to be stable.

[0227] (2) Wind speed change in the wind farm

[0228] In view of the fact that the wind speed in the wind farm is variable, which is manifested as the fluctuation of the wind farm output, it is necessary to study the adaptability of the active disturbance rejection control to the wind speed. Set three different wind speeds, keep other parameters and operating conditions unchanged, and study the ability of the active disturbance rejection controller to suppress subsynchronous oscillation of the VSG connected to the grid system. The active power output response diagram of the wind farm is as Figure 13 shown (where, Figure 13 Among them, ADRC control is the improved active disturbance rejection controller of the present invention). It can be analyzed that when the wind speed changes from 11 m / s to 9 m / s, subsynchronous oscillation phenomena will occur in the wind farm under PI control, and the oscillation intensity decreases with the increase of the wind speed; while when using the active disturbance rejection control, the change of the wind speed has little effect on the suppression effect of the active disturbance rejection control, and it can effectively weaken the oscillation jitter amplitude at the initial stage of oscillation, and then quickly suppress the oscillation, so as to ensure the stable and safe operation of the whole system.

[0229] (3) Change of ground short-circuit fault

[0230] Since the ground short-circuit fault is a kind of disturbance and has the ability to induce subsynchronous oscillation in the system. Therefore, set the line series compensation to the input state, keep other parameters constant, and verify the adaptability of the active disturbance rejection controller to different ground short-circuit faults. When the system enters the steady state, set different ground short-circuit faults on the 690V / 35kV high-voltage side at 8s, and the fault duration is close to 0.2s. The active power output response curves of the wind farm under different ground short-circuit faults are as Figure 14 shown (where, Figure 14 Among them, ADRC control is the improved active disturbance rejection controller of the present invention). It can be seen that under the ground short-circuit fault, the active power output P w of the wind farm based on PI control quickly undergoes divergent oscillation. Subsequently, when the controller enters the limiter region, P w shows continuous equal-amplitude oscillation, and the system shows an unstable state, and subsynchronous oscillation occurs; while when using the improved ADRC control, after the fault, P wAfter experiencing a short transient process, they can all resume normal operation and effectively suppress the occurrence of subsynchronous oscillation. Thus, it can be seen that the ADRC control has good suppression ability for subsynchronous oscillation under grounding short-circuit faults.

[0231] Embodiment 2: A subsynchronous oscillation suppression system for a virtual synchronous doubly-fed wind turbine connected to the grid through series compensation, comprising: a first construction module for placing the Fal function filter after the output of the virtual synchronous doubly-fed wind turbine connected to the grid through series compensation and constructing an extended extended state observer together with the traditional extended state observer (ESO); a second construction module for constructing an improved active disturbance rejection controller based on the extended extended state observer and the linear error feedback (LSEF); and a suppression module for suppressing the subsynchronous oscillation of the virtual synchronous doubly-fed wind turbine connected to the grid through series compensation by using the improved active disturbance rejection controller.

[0232] Furthermore, it further comprises: a verification module for verifying the subsynchronous oscillation suppression effect of the proposed improved active disturbance rejection controller strategy under different disturbance conditions.

[0233] The serial numbers of the above embodiments of the present invention are only for description and do not represent the advantages and disadvantages of the embodiments.

[0234] In the above embodiments of the present invention, the descriptions of the respective embodiments have their own emphases. For the parts not detailed in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0235] The specific embodiments of the present invention have been described in detail above in conjunction with the accompanying drawings. However, the present invention is not limited to the above embodiments, and various changes can be made without departing from the spirit of the present invention within the scope of knowledge possessed by those of ordinary skill in the art.

Claims

1. A method for suppressing subsynchronous oscillation of a virtual synchronous doubly-fed wind turbine connected to the grid through series compensation, characterized in that, Including: Obtain the output impedance expression of the grid-side converter based on VSG; From the perspective of the equivalent impedance of the doubly-fed wind turbine grid-connected system, reveal the positive damping characteristics of the grid-side converter based on VSG against subsynchronous oscillation; Combine active disturbance rejection control to analyze the subsynchronous oscillation suppression mechanism of the virtual synchronous doubly-fed wind turbine grid-connected system; Construct an improved active disturbance rejection controller to suppress subsynchronous oscillation; The obtaining of the output impedance expression of the grid-side converter based on VSG includes: S1.

1. Adopt the small-signal stability analysis method of the power system, and linearize the dynamic equation of VSG based on the control topology structure of VSG. The mathematical expression of its linearization result is: Among them, F PQ , F PI , F1, F2, F L are all 2×2 transfer function matrices; T J and D p are the moment of inertia and damping coefficient respectively; K p and K i are the excitation control proportional coefficient and integral coefficient respectively; K v is the reactive power-voltage control droop coefficient; s is the Laplace operator; K Vp1 and K Vi1 are the d-axis proportional coefficient and integral coefficient of the VSG output voltage control respectively; K Vp2 and K Vi2 are the q-axis proportional coefficient and integral coefficient of the VSG output voltage control respectively; I sd and I sq are the d-axis component and q-axis component of the steady-state quantity of the stator current in the synchronous rotating coordinate system respectively; U sd and U sq are the d-axis component and q-axis component of the steady-state operating point of the stator voltage in the synchronous rotating coordinate system respectively; E m is the excitation control output voltage; δ is the difference between the phase angle output by the phase-locked loop and the phase of the grid-connected system voltage; L is the filter inductor; U g is the stable value of the grid-side voltage; ω N is the synchronous angular velocity; S1.

2. Obtain the VSG control parameters and system network operation parameters in the steady state, and take the dq rotating coordinate system as the reference system to obtain the output impedance expression of the grid-side converter based on VSG as: Among them, [Δu sd , Δu sq T is the stator side voltage disturbance vector of the grid-connected system; [Δi sd , Δi sq T is the stator side current response vector of the grid-connected system; Z out is the output impedance of the grid-side converter based on VSG; Z dd , Z dq , Z qd and Z qq respectively represent the d-d, d-q, q-d and q-q axis components of the output impedance Z out ; I represents the identity matrix.​​ 2. The method for suppressing subsynchronous oscillation of a virtual synchronous doubly-fed wind turbine connected to the grid through series compensation according to claim 1, wherein: The revealing of the positive damping characteristics of the grid-side converter based on VSG against subsynchronous oscillation from the perspective of the equivalent impedance of the doubly-fed wind turbine grid-connected system includes: S2.

1. Equivalent output impedance Z of doubly-fed wind turbines G The mathematical expression is as follows: Among them, R G and X G are the equivalent resistance and reactance of the doubly-fed induction generator (DFIG), respectively; R s is the sum of the stator winding resistance of the DFIG and the resistance of the transformer; R r is the resistance of the rotor winding; R RSC represents the equivalent resistance of the rotor-side converter; L ls is the sum of the leakage inductance of the stator winding of the DFIG and the transformer; L lr is the rotor leakage inductance; L m is the excitation inductance; the slip ratio f r and j represent the rotor frequency and the imaginary unit, respectively; the resonant frequency of the inductance and capacitance series resonance circuit ω ss and f0 are the resonant frequency of the equivalent series circuit of the system under subsynchronous oscillation and the system base frequency, respectively; X C and X L are the capacitive reactance of the series capacitor and the equivalent reactance of the system, respectively. S2.

2. After the grid-side converter of the doubly-fed wind turbine is controlled by the VSG, the equivalent output impedance Z of the doubly-fed wind turbine based on the VSG is obtained. G1 The expression is as follows: Among them, R VSG and X VSG are the equivalent resistance and reactance of the VSG respectively; R G1 and X G1 are the equivalent resistance and reactance of the doubly-fed wind turbine after connecting the VSG respectively.

3. The method for suppressing subsynchronous oscillation of a virtual synchronous doubly-fed wind turbine connected to the grid through series compensation according to claim 1, wherein: The combining of active disturbance rejection control to analyze the subsynchronous oscillation suppression mechanism of the virtual synchronous doubly-fed wind turbine grid-connected system includes: Taking the d-axis analysis as an example, obtain the mathematical expression of the output voltage of the current inner loop of the grid-side converter under the access of VSG as: Among them, u gd is the d-axis component of the output voltage of the grid-side converter; R g and L g are the resistance and inductance of the grid-side incoming line reactor respectively; i gd and i gq are the d-axis and q-axis components of the grid input current respectively; ω N is the synchronous angular velocity; E VSGd is the d-axis component of the VSG output voltage; When the grid-connected system has a subsynchronous oscillation, the expression of the output voltage of the current inner loop of the grid-side converter under the disturbance is rewritten as: where, Δu sub_gd and ΔE sub_VSGd are the output sub-synchronous voltage of the grid-side converter and the d-axis component of the VSG output sub-synchronous voltage under perturbation, respectively; Δi sub_gd and Δi sub_gq are the d- and q-axis components of the sub-synchronous current, respectively; Analyze the influence law of the PI control parameters of the current inner loop of the grid-side converter on subsynchronous oscillation, and obtain the mathematical expression of the output voltage of the current inner loop of the grid-side converter based on PI control as: where K p2 and K i2 are respectively the d-axis proportional coefficient and integral coefficient of the PI controller in the current inner loop control of the grid-side converter; s is the Laplace operator; When the grid-connected system operates stably, obtain the d-axis current expression of the grid-side converter under VSG control as: When there are subsynchronous oscillation components in the system, the subsynchronous oscillation flows through the control link of the grid-side converter in the form of subsynchronous current and voltage components, resulting in the d-axis current of the grid-side converter becoming: The equation transformation is as follows: where f1(Δi sub_gd , Δi sub_gq ) is the d-axis component of the subsynchronous current in the grid-connected system; Before and after using the active disturbance rejection controller, obtain the mathematical expression of the d-axis current of the grid-side converter as: The q-axis is the same by analogy.

4. The method for suppressing subsynchronous oscillation of a virtual synchronous doubly-fed wind turbine connected to the grid through series compensation according to claim 1, characterized in that: The constructing of the improved active disturbance rejection controller includes: S4.

1. To suppress the subsynchronous oscillation of the doubly-fed wind turbine grid-connected system under VSG control, replace the PI controller of the current inner loop of the grid-side converter with the active disturbance rejection controller, then the mathematical expression of the current of the grid-side converter is rewritten as: wherein, i gd and i gq are respectively the d-axis and q-axis components of the grid input current; u gd and u gq are respectively the d-axis and q-axis components of the output voltage of the grid-side converter; b d and b q are respectively the d-axis and q-axis components of the dynamic compensation factor; f1(Δi sub_gd , Δi sub_gq ) is the d-axis component of the subsynchronous current in the grid-connected system; f2(Δi sub_gd , Δi sub_gq ) represents the q-axis component of the subsynchronous current in the grid-connected system; R g and L g are respectively the resistance and inductance of the grid-side incoming line reactor; ω N is the synchronous angular velocity; E VSGd is the d-axis component of the VSG output voltage; It can be seen that there is coupling between the d-axis and q-axis of the current inner loop control of the grid-side converter; to achieve precise decoupling control of the output current of the grid-side converter, include the coupling term in the disturbance, then it becomes: where, F1(Δi sub_gd , Δi sub_gq ) and F2(Δi sub_gd , Δi sub_gq ) are respectively the d-axis component and the q-axis component of the total sub-synchronous disturbance amount and coupling amount controlled by the grid-side converter; S4.

2. The construction of the improved active disturbance rejection controller includes: an extended extended state observer, a linear error feedback LSEF; S4.

3. Performance analysis of the improved active disturbance rejection controller.

5. The method for suppressing subsynchronous oscillation of a virtual synchronous doubly-fed wind turbine connected to the grid through series compensation according to claim 4, wherein The extended extended state observer ESO is to place the Fal function filter after the output of the virtual synchronous doubly-fed wind turbine connected to the grid through series compensation, and form an extended extended state observer together with the traditional extended state observer ESO.

6. The method for suppressing subsynchronous oscillation of a virtual synchronous doubly-fed wind turbine connected to the grid through series compensation according to claim 1, wherein It also includes a verification step: verify the subsynchronous oscillation suppression effect of the proposed improved active disturbance rejection controller strategy under different disturbance conditions.

7. The method for suppressing subsynchronous oscillation of a virtual synchronous doubly-fed wind turbine connected to the grid through series compensation according to claim 6, wherein The different disturbance conditions include: different numbers of wind turbines, wind farm wind speeds, series compensation degrees, and grounding fault types.

Images