A small signal model modeling method and device of a doubly-fed wind power grid-connected system under alternating current asymmetric working conditions

Abstract

The application discloses a kind of small signal model modeling method and equipment of double-fed wind power grid-connected system under AC asymmetric condition. Including the following steps: the nonlinear periodic time-varying dynamic model of mechanical system is established, the original nonlinear periodic time-varying dynamic model of electrical system and the nonlinear periodic time-varying dynamic model of control system;The original nonlinear periodic time-varying dynamic model of electrical system is carried out dq-sequence dynamic phasor transformation, and the key variable dominant frequency component is retained, to obtain the simplified nonlinear periodic time-varying dynamic model of electrical system;The nonlinear periodic time-varying dynamic model of mechanical system, the nonlinear periodic time-varying dynamic model of control system and the simplified nonlinear periodic time-varying dynamic model of electrical system are linearized on the steady-state periodic trajectory, integrated and eliminated algebraic variable, to obtain the linear periodic time-varying small signal model of double-fed wind power grid-connected system, the application provides modeling basis for wideband oscillation analysis of wind power system under asymmetric condition.

Description

Technical Field

[0001] This invention belongs to the field of doubly-fed induction generator modeling, and more specifically, relates to a small-signal modeling method and equipment for a doubly-fed wind power grid-connected system under AC asymmetric operating conditions. Background Technology

[0002] Doubly fed induction generators (DFIGs) are currently the mainstream commercial wind turbine type. Wind power systems are essentially high-order, nonlinear, and strongly coupled converter power sources, exhibiting complex dynamic interactions with the power grid. Under certain conditions, this can induce broadband oscillations, threatening system stability and power quality. For power electronics-dominated oscillation problems, small-signal stability modeling primarily employs linear time-varying periodic (LTP) or linear time-invariant (LTI) models. The LTP method preserves the system's time-varying characteristics without increasing the model order, resulting in high modeling accuracy, but its mathematical form is complex. The LTI method uses constant elements in the state matrix and has a more mature stability analysis theory, but it requires truncating the spectrum, which can introduce errors and increase the model order.

[0003] Existing research is largely based on the assumptions of three-phase balance and positive-sequence control, which makes it difficult to reflect the dynamic characteristics of actual wind power grid-connected systems under grid voltage asymmetry. On the one hand, motor winding parameters exhibit significant periodic time-varying characteristics under asymmetrical operating conditions, making it difficult for traditional LTP modeling to decouple the motor winding current and flux linkage state equations, resulting in high modeling complexity. On the other hand, voltage imbalance introduces negative-sequence components and second-harmonic disturbances into key variables, and phase sequence separation and negative-sequence control also exist in the control system. LTI modeling cannot accurately describe the derived second-harmonic periodic components in key variables and the transient processes of the control system, leading to insufficient accuracy. Existing LTI methods neglect the second-harmonic components in electromagnetic torque and DC capacitor voltage in the main circuit modeling, and also fail to model the phase sequence separation and second-harmonic components in the outer-loop control variables in the control system, exhibiting significant limitations. Currently, there is a lack of complete LTP modeling research for DFIG grid-connected systems under asymmetrical operating conditions.

[0004] The prior art patent CN117559529A proposes a dynamic phasor domain dq transformation method for small-disturbance analysis of direct-drive wind turbine grid connection. It establishes expressions for the wind turbine's electrical and control systems in dynamic phasor form. For the direct-drive wind turbine converter control part in the dq coordinate system, the Parker transformation matrix is ​​reconstructed and transformed to the abc coordinate system based on the definition of dynamic phasors. On this basis, an equivalent model of the power system containing the wind turbine is established and linearized. The impact of wind turbine grid connection on system stability is further studied. However, this scheme only considers the direct-drive wind turbine structure, does not consider the elastic-torsional coupling of the mechanical shaft system, and only applies the LTI approximation, neglecting negative-sequence / second harmonic coupling. Summary of the Invention

[0005] This invention aims to overcome the problems of existing small-signal modeling methods under asymmetrical operating conditions, including the failure to consider the second harmonic disturbance components in the generator electromagnetic torque and the DC capacitor voltage of the power converter, the neglect of phase sequence separation modeling in the control system, and the influence of the second harmonic component in the outer loop control variables of the current vector. It provides a small-signal modeling method and device for a doubly fed wind power grid-connected system under AC asymmetrical operating conditions.

[0006] The primary objective of this invention is to solve the aforementioned technical problems. The technical solution of this invention is as follows:

[0007] The first aspect of this invention provides a small-signal modeling method for a doubly-fed induction generator (DFIG) wind power grid-connected system under AC asymmetric operating conditions, comprising the following steps:

[0008] Establish nonlinear periodic time-varying dynamic models of mechanical systems, original nonlinear periodic time-varying dynamic models of electrical systems, and nonlinear periodic time-varying dynamic models of control systems;

[0009] The original nonlinear periodic time-varying dynamic model of the electrical system is subjected to dq-order dynamic phasor transformation, and the dominant frequency components of key variables are retained to obtain a simplified nonlinear periodic time-varying dynamic model of the electrical system.

[0010] The nonlinear periodic time-varying dynamic model of the mechanical system, the nonlinear periodic time-varying dynamic model of the control system, and the simplified nonlinear periodic time-varying dynamic model of the electrical system are linearized on the steady-state periodic trajectory. The algebraic variables are then integrated and eliminated to obtain the linear periodic time-varying small-signal model of the doubly-fed wind power grid-connected system.

[0011] Furthermore, the original nonlinear periodic time-varying dynamic model of the electrical system includes an induction generator model, an AC-DC-AC power converter model, and a grid-connected filter circuit model, which are established based on the following physical relationships:

[0012] A primitive nonlinear periodic time-varying dynamic model of an induction generator is established using the three-phase voltage balance equation, flux linkage equation, and electromagnetic torque equation of the stator / rotor of the induction generator.

[0013] The original model of the AC-DC-AC power converter is established using the DC-side power balance equation, the converter modulation signal expression, and the relationship between the AC output voltage and DC voltage of the converter.

[0014] The original model of the grid-connected filter circuit is established using the current-voltage relationship equation of the grid-connected filter circuit.

[0015] Furthermore, the simplified nonlinear periodic time-varying dynamic model of the electrical system includes: a dynamic phasor model of the induction generator, a dynamic phasor model of the converter, and a dynamic phasor model of the grid-connected filter circuit. The original nonlinear periodic time-varying dynamic model of the electrical system is subjected to dq-sequence dynamic phasor transformation to obtain the simplified nonlinear periodic time-varying dynamic model of the electrical system, including the following steps:

[0016] The original nonlinear periodic time-varying dynamic model of the induction generator is subjected to dq-sequence dynamic phasor transformation to output the dynamic phasor model of the induction generator.

[0017] The original AC-DC-AC power converter model is subjected to dq-sequence dynamic phasor transformation to output the converter dynamic phasor model.

[0018] The original model of the grid-connected filter circuit is subjected to dq-sequence dynamic phasor transformation to output the dynamic phasor model of the grid-connected filter circuit.

[0019] Furthermore, when performing dq-sequence dynamic phasor transformation on the original nonlinear periodic time-varying dynamic model of the induction generator, the electromagnetic torque retains DC and second harmonic components, the stator voltage and current retain positive and negative sequence fundamental frequency components, and the rotor voltage and current retain positive sequence s harmonic and negative sequence (2-s) harmonic components, where s is the slip.

[0020] When performing dq-sequence dynamic phasor transformation on the original AC-DC-AC power converter model, the DC capacitor voltage retains the DC and second harmonic components, the grid-side current and GSC modulation signal retain the positive and negative fundamental frequency components, and the rotor current and RSC modulation signal retain the positive s harmonic and negative (2-s) harmonic components.

[0021] When performing dq-sequence dynamic phasor transformation on the original model of the grid-connected filter circuit, the DC capacitor voltage retains the DC and second harmonic components, while the grid-side voltage, grid-side current, and GSC modulation signal retain the positive and negative sequence fundamental frequency components.

[0022] Furthermore, the converter modulation signal expression includes the modulation signal expression of the rotor-side converter RSC and the modulation signal expression of the grid-connected converter GSC.

[0023] Furthermore, the nonlinear periodic time-varying dynamic model of the control system includes models of the phase-locked loop and phase sequence separation element in the time domain, a rotor-side control model, and a grid-connected side control model, which are established based on the following physical relationships:

[0024] A time-domain model of the phase-locked loop and phase sequence separation element is established using a phase-locked loop and a complex filter.

[0025] A rotor-side control model is established using a cascaded proportional-integral regulator control strategy for the power outer loop and current inner loop of the rotor-side converter, and a negative-sequence current vector control strategy.

[0026] A grid-connected control model is established using a cascaded proportional-integral regulator control strategy for the outer voltage loop and inner current loop of the grid-connected converter, and a negative sequence current vector control strategy.

[0027] Furthermore, the phase-locked loop is a first-order proportional-integral (PII) phase-locked loop.

[0028] Furthermore, the complex filter is a multi-complex filter.

[0029] Furthermore, the linear periodic time-varying small signal model is a 47th-order state-space model.

[0030] The second aspect of the present invention provides a small-signal modeling device for a doubly-fed induction generator (DFIG) grid-connected wind power system under AC asymmetric operating conditions, comprising a memory and a processor. The memory includes a small-signal modeling method program for the DFIG grid-connected wind power system under AC asymmetric operating conditions. When the processor executes the small-signal modeling method program for the DFIG grid-connected wind power system under AC asymmetric operating conditions, it implements the steps of a small-signal modeling method for the DFIG grid-connected wind power system under AC asymmetric operating conditions.

[0031] Compared with the prior art, the beneficial effects of the technical solution of the present invention are:

[0032] This invention establishes a small-signal state-space model for a doubly-fed induction generator (DFIG) grid-connected wind power system applicable to three-phase unbalanced operation, considering negative-sequence control, and covering wide-bandwidth disturbance characteristics. For the electrical system, a dq-sequence dynamic phasor modeling method is employed, performing equivalent LTI processing on the induction motor, converter, etc., explicitly considering the second harmonic disturbance components in the electromagnetic torque and DC capacitor voltage. For the mechanical and control systems, an LTP modeling method is used, retaining the dominant frequency components in key variables, accurately characterizing the phase sequence separation mechanism and the current vector outer-loop control characteristics. Through the coupling and integration of the LTI and LTP models, a generalized LTP small-signal model of the DFIG grid-connected system with unified structure and accurate frequency expression is constructed, providing a modeling foundation for wide-bandwidth oscillation analysis of wind power systems under asymmetrical operating conditions. Attached Figure Description

[0033] To make the objectives and technical solutions of this invention clearer, the following drawings are provided and described:

[0034] Figure 1 A flowchart of the method provided in an embodiment of the present invention;

[0035] Figure 2 This is the topology of the doubly fed induction motor grid-connected system provided in the embodiments of the present invention;

[0036] Figure 3A structural diagram of a PLL provided in an embodiment of the present invention;

[0037] Figure 4 A structural diagram of the MCCF provided in an embodiment of the present invention;

[0038] Figure 5 A structural diagram of the rotor-side positive sequence current vector controller provided in an embodiment of the present invention;

[0039] Figure 6 A structural diagram of the rotor-side negative sequence current vector controller provided in an embodiment of the present invention;

[0040] Figure 7 A structural diagram of the grid-side positive sequence current vector controller provided in an embodiment of the present invention;

[0041] Figure 8 A structural diagram of the grid-side negative sequence current vector controller provided in an embodiment of the present invention;

[0042] Figure 9 This is a diagram showing the verification results of a small-signal model for wind speed variation under asymmetrical operating conditions of an AC system, provided in an embodiment of the present invention.

[0043] Figure 10 The figure shows the verification results of the small-signal model under DC voltage step conditions in an AC system according to an embodiment of the present invention.

[0044] Figure 11 The response curve of the negative sequence d-axis component of the rotor current during the kp7 step provided in this embodiment of the invention. Detailed Implementation

[0045] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in these embodiments can be combined with each other.

[0046] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and therefore the scope of protection of the invention is not limited to the specific embodiments disclosed below.

[0047] Example 1:

[0048] This invention provides a small-signal modeling method for a doubly-fed induction generator (DFIG) wind power grid-connected system under AC asymmetric operating conditions, such as... Figure 1 The diagram shows a flowchart of a small-signal modeling method for a doubly-fed induction generator (DFIG) grid-connected wind power system under AC asymmetric operating conditions. The topology of the DFIG grid-connected system is shown below. Figure 2As shown, it mainly includes mechanical systems (wind turbine, mechanical transmission system), electrical systems (DFIG, AC-DC-AC power converter, grid-side filter circuit, transformer), and control systems (phase-locked loop (PLL), rotor-side converter (RSC) control system, grid-side converter (GSC) control system, etc.). In the figure, i sj , i rj For the stator and rotor currents of the DFIG; i gj This refers to the current in the grid-side filter circuit. C It is a DC capacitor; P r , P 1 represents the power output of the DC capacitor to the RSC and GSC; u ri and u tj The output voltages for RSC and GSC are the three-phase AC voltages. This is the voltage of the DC capacitor; u gj This refers to the three-phase AC voltage of the power grid. , These are the filter resistor and inductor, respectively. This represents the output angle of the phase-locked loop. Among the variables mentioned above, j = a, b, and c represent phases a, b, and c, respectively.

[0049] The specific steps of this invention are as follows:

[0050] S1: Establish a nonlinear periodic time-varying dynamic model for the mechanical system, an original nonlinear periodic time-varying dynamic model for the electrical system, and a nonlinear periodic time-varying dynamic model for the control system.

[0051] A nonlinear periodic time-varying dynamic model of the mechanical system is established, as shown in equations (1)-(2). The mathematical model of the wind turbine is shown in expression (1):

[0052] (1)

[0053] in, and These are the mechanical power and mechanical torque output by the wind turbine, respectively. air density; Where is the blade radius; Wind speed; The wind energy conversion coefficient is related to the tip speed ratio. The function; This represents the mechanical angular velocity of the wind turbine.

[0054] The mathematical model of the mechanical transmission system is shown in expression (2):

[0055] (2)

[0056] in, and These are the moments of inertia of the wind turbine and the generator, respectively. and These are the equivalent mechanical angular velocity of the wind turbine and the mechanical angular velocity of the generator rotor, respectively. The equivalent torque of the wind turbine, , This refers to the gearbox transmission ratio; The electromagnetic torque of the generator, when the AC power grid is unbalanced. It contains a relatively significant second harmonic component. This represents the real part of the DC component in the electromagnetic torque. , These represent the real and imaginary parts of the second harmonic component in the electromagnetic torque. and The damping coefficients for the wind turbine and generator; This is the equivalent stiffness coefficient of the shaft system; The angle of torsion of the shaft system; This represents the angular velocity corresponding to the grid frequency.

[0057] More specifically, the nonlinear periodic time-varying dynamic model of the control system includes the time-domain models of the phase-locked loop and phase sequence separation element, the rotor-side control model, and the grid-connected side control model, which are established based on the following physical relationships:

[0058] A phase-locked loop and a phase sequence separation stage are modeled in the time domain using a first-order proportional-integral (PI) phase-locked loop and a multiple repetition filter (MCCF), as shown in equations (12)-(13).

[0059] The structural block diagram of the PLL is as follows: Figure 3 As shown, its time-invariant mathematical model is expressed by equation (12).

[0060] (12)

[0061] in, These are the state variables of the phase-locked loop; ; and These are the proportional and integral coefficients of the PLL, respectively. The angular frequency calculated by the phase-locked loop. The stator voltage separated by the phase sequence separation stage u s Positive sequence fundamental frequencyq Axial components.

[0062] Adopting such Figure 4 The Multiple Complex Coefficient Filter (MCCF) shown extracts the stator voltage. and current Rotor current Current of the grid-side filter circuit The positive and negative sequence fundamental frequency components. , yes AC electrical quantities in a coordinate system , , , They are after separation Positive and negative sequence components of AC electrical quantities in a coordinate system. , , , They are after separation dq Positive and negative sequence components of AC electrical quantities in a coordinate system.

[0063] Taking the stator current as an example, the time-varying mathematical model of its phase sequence separation stage is shown in equation (13). Stator voltage Rotor current Current of the grid-side filter circuit The same applies to the phase sequence separation process.

[0064] (13)

[0065] in, The cutoff frequency; , and , The stator current separated by the phase sequence separation stage Positive and negative fundamental frequencies d, q Axial components, For the complex components in the positive d-axis direction, For the complex components along the positive q-axis, For the complex components in the negative d-axis direction, For the complex components along the negative q-axis, Provides a reference angle for the rotating coordinate system of the phase-locked loop (PLL).

[0066] The rotor-side control model is established using the cascade proportional-integral regulator control strategy of the power outer loop and current inner loop of the rotor-side (RSC) converter and the negative sequence current vector control strategy, as shown in equations (14)-(15).

[0067] The RSC positive sequence current vector controller uses stator voltage-oriented vector control to orient the stator voltage to... d The shaft, its structural block diagram is as follows Figure 5 As shown, the time-varying mathematical model is described by equation (14).

[0068] (14)

[0069] in, , , , For the positive sequence current vector controller of RSC; and These are reference values ​​for active power and reactive power on the stator side, respectively. In the secondary synchronization state, Set as In hypersynchronous state, Set as ; The optimal wind energy conversion coefficient; The optimal tip speed ratio; and These are the active power and reactive power output from the stator side as measured by the control system. , , These represent the real part, the real part, and the imaginary part of the stator active DC component. , , These are the real part, the real part, and the imaginary part of the stator reactive DC component; , , , and , , , For the proportional and integral coefficients of the RSC dual closed-loop control; The leakage coefficient is given by... Calculate, for dq Mutual inductance between equivalent stator and rotor windings in the coordinate system , For stator and rotor leakage inductance, , ; and These are reference values ​​for the rotor's positive sequence d-axis and q-axis voltages; and These are the stator positive sequence values ​​in the control system. d, q Axial magnetic flux, The reference angular frequency is t, where t is the time variable. This refers to the positive-sequence d-axis component of the rotor current separated by the phase sequence separation stage. This is the positive sequence d-axis reference value for the rotor-side converter output voltage. This is the positive-sequence d-axis control quantity for the rotor-side converter output voltage. This is the positive-sequence q-axis control quantity for the output voltage of the rotor-side converter. This refers to the positive-sequence d-axis component of the stator voltage separated by the phase sequence separation stage. This refers to the positive-sequence q-axis component of the stator voltage separated by the phase sequence separation stage. This is the angular frequency of the phase-locked loop output. The rotor angular frequency, This refers to the positive-sequence q-axis component of the rotor current separated by the phase sequence separation stage. The positive sequence d-axis component of the rotor current separated by the phase sequence separation stage.

[0070] The block diagram of the RSC negative sequence current vector controller is as follows: Figure 6 As shown, the time-invariant mathematical model is described by equation (15).

[0071] (15)

[0072] in, , For the negative sequence current vector controller of RSC; , and , These are the proportional and integral coefficients for rotor negative sequence current control; and For rotor negative sequence d , q Reference value for shaft current; and For rotor negative sequence d , q Reference value for shaft voltage; and These are the stator negative sequence in the control system. d, q Axial magnetic flux, This refers to the negative-sequence q-axis component of the rotor current separated by the phase sequence separation stage. The negative sequence d-axis component of the rotor current separated by the phase sequence separation stage. The negative sequence d-axis control quantity for the rotor-side converter output voltage. This is the negative-sequence q-axis control quantity for the rotor-side converter output voltage. The negative sequence d-axis component of the stator voltage separated by the phase sequence separation stage. This refers to the negative-sequence q-axis component of the stator voltage separated by the phase sequence separation stage.

[0073] A grid-connected control model is established using the voltage outer loop and current inner loop cascade proportional-integral regulator control strategy and the negative sequence current vector control strategy of the grid-connected (GSC) converter, as shown in equations (16)-(17).

[0074] The GSC positive sequence current vector controller employs grid voltage-oriented control, meaning its d-axis is oriented to the grid voltage vector. Its block diagram is shown below. Figure 7 As shown, the time-varying mathematical model is described by equation (16).

[0075] (16)

[0076] in, , , For the positive sequence current vector controller of GSC; This is a reference value for the DC capacitor voltage; , , For each component of the DC capacitor voltage, there are the real part, the real part, and the imaginary part of the second harmonic component. , The proportional-integral coefficient of the outer voltage loop; , Positive sequence current on the grid side d Proportional and integral coefficients of the inner loop control of the shaft component; , For the net side positive sequence q Proportional and integral coefficients for shaft current inner loop control; Positive sequence current on the grid side q Reference values ​​for axis components; and For GSC export positive sequence d , q Reference value for shaft voltage; and The positive sequence of the power grid separated by the phase sequence separation stage d, q shaft voltage, This represents the positive-sequence d-axis component of the output current of the grid-side filter inductor separated by the phase sequence separation stage. This refers to the positive-sequence q-axis component of the output current of the grid-side filter inductor separated by the phase sequence separation stage.

[0077] The block diagram of the GSC negative sequence current vector controller is as follows: Figure 8 As shown, the time-invariant mathematical model is described by equation (17).

[0078] (17)

[0079] in, , For the negative sequence current vector controller of GSC; , and , Negative sequence on the network side d, q Proportional and integral coefficients for shaft current control; and Negative sequence for network side d , q Reference value for shaft current; and For GSC export negative sequence d , q Reference value for shaft voltage; and The negative sequence of the power grid output for the phase sequence separation stage d, q Shaft voltage.

[0080] It should be noted that the above mechanical and control system equations all contain time variables. t Therefore, they are all nonlinear periodic time-varying models.

[0081] More specifically, the original nonlinear periodic time-varying dynamic model of the electrical system includes an induction generator model, an AC-DC-AC power converter model, and a grid-connected filter circuit model, which are established based on the following physical relationships:

[0082] The original nonlinear periodic time-varying dynamic model of the induction generator is established using the three-phase voltage balance equation, flux linkage equation and electromagnetic torque equation of the stator / rotor of the induction motor, as shown in equations (3)-(6).

[0083] The voltage balance equation for the three-phase stator winding is:

[0084] (3)

[0085] The voltage balance equation for the three-phase rotor windings referred to the stator side is:

[0086] (4)

[0087] in, , , and , , The instantaneous phase voltages of each phase of the stator and rotor; , , and , , For the magnetic flux linkages of each phase winding of the stator and rotor; , The resistance of each phase winding of the stator and rotor; , , and , , This refers to the instantaneous phase current of the stator and rotor windings.

[0088] The magnetic flux linkages in equations (3) and (4) satisfy the following equations:

[0089] (5)

[0090] in, and These are the self-inductances of each phase winding of the stator and rotor, respectively; , and These are the mutual inductance between stators, the mutual inductance between rotors, and the mutual inductance between stators and rotors, respectively. This is the rotor position angle.

[0091] The electromagnetic torque of the induction generator satisfies:

[0092] (6)

[0093] in, This represents the number of pole pairs of the motor.

[0094] The original model of the AC-DC-AC power converter is established using the DC-side power balance equation, the converter modulation signal expression, and the relationship between the AC output voltage and the DC voltage of the converter.

[0095] More specifically, the converter modulation signal expression includes the modulation signal expression of the rotor-side converter RSC and the modulation signal expression of the grid-connected converter GSC, as shown in equations (7)-(10).

[0096] (7)

[0097] in, , , Where is the instantaneous phase voltage of each phase of the rotor, and C is the DC bus capacitance. The voltage across the intermediate DC capacitor in the AC-DC-AC converter. , , The three-phase AC voltages at the grid-side converter outlets a, b, and c are... , , These are the a, b, and c phase currents flowing from the grid-side filter circuit towards the power grid.

[0098] The modulated signals of RSC and GSC can be described by equations (8) and (9).

[0099] (8)

[0100] in, , , The modulation signals for phases a, b, and c of the rotor-side converter are... Let be the fundamental angular frequency of the power grid, and t be the time variable. , These represent the modulation ratio and phase shift angle of the negative sequence modulation signal in the rotor-side converter, respectively. , These represent the modulation ratio and phase shift angle of the positive sequence modulation signal of the rotor-side converter, respectively. ω is the rotor rotational angular velocity.

[0101] (9)

[0102] in, , These represent the modulation ratio and phase shift angle of the positive sequence modulation signal of the grid-side converter, respectively. , These represent the modulation ratio and phase shift angle of the negative sequence modulation signal of the grid-side converter, respectively. , , The modulation signals for phases a, b, and c of the grid-side converter;

[0103] Both RSC and GSC use space vector pulse width modulation.

[0104] (10)

[0105] The original model of the grid-connected filter circuit is established using the current-voltage relationship equation of the grid-connected filter circuit, as shown in equation (11).

[0106] (11)

[0107] in, For grid-side filter inductance, For grid-side filter resistors, , , The voltages of phases a, b, and c at the point of connection to the power grid are given.

[0108] S2: Perform dq-order dynamic phasor transformation on the original nonlinear periodic time-varying dynamic model of the electrical system, retain the dominant frequency components of key variables, and obtain a simplified nonlinear periodic time-varying dynamic model of the electrical system.

[0109] More specifically, the simplified nonlinear periodic time-varying dynamic model of the electrical system includes: a dynamic phasor model of the induction generator, a dynamic phasor model of the converter, and a dynamic phasor model of the grid-connected filter circuit. The original nonlinear periodic time-varying dynamic model of the electrical system is subjected to dq-sequence dynamic phasor transformation to obtain the simplified nonlinear periodic time-varying dynamic model of the electrical system, including the following steps:

[0110] The original nonlinear periodic time-varying dynamic model of the induction generator is subjected to dq-sequence dynamic phasor transformation to output the dynamic phasor model of the induction generator. In this model, the electromagnetic torque retains the DC and second harmonic components, the stator voltage and current retain the positive and negative sequence fundamental frequency components, and the rotor voltage and current retain the positive sequence s-harmonic and negative sequence (2-s) harmonic components, where s is the slip. .

[0111] use dq - The order dynamic phasor modeling method converts (3)-(6) into dq The time-invariant model of the order dynamic phasor is shown in equations (18)-(21).

[0112] (18)

[0113] (19)

[0114] (20)

[0115] (twenty one)

[0116] In this context, the superscripts +, -, and 0 of all dynamic phasors represent positive, negative, and zero order, respectively; the numbers within the subscripts () (including) s and 2- s () indicates frequency, s is slip; subscript d , q express d , q Axis components; subscripts excluding the first one r , i This indicates the real and imaginary parts of the phasor corresponding to the variable. For stator current, Stator voltage, For stator resistance, For rotor current, For rotor voltage, For rotor resistance, For mutual inductance between stator and rotor, For the self-sensing of the stator, Let σ be the rotor self-inductance, σ be the leakage flux coefficient, ω be the grid angular frequency, ωr be the rotor angular frequency, and t be the time variable. This represents the real part of the DC component in the electromagnetic torque. This represents the real part of the second harmonic component in the electromagnetic torque. This represents the imaginary part of the second harmonic component in the electromagnetic torque. p It is a polar logarithm. For example: Represents stator current positive sequence fundamental frequency d Axial components, and so on.

[0117] The original AC-DC-AC power converter model is subjected to dq-sequence dynamic phasor transformation to output the converter dynamic phasor time-varying model. In this model, the DC capacitor voltage retains the DC and second harmonic components, the grid-side current and GSC modulation signal retain the positive and negative fundamental frequency components, and the rotor current and RSC modulation signal retain the positive s harmonic and negative (2-s) harmonic components, as shown in equations (22) and (23).

[0118] (twenty two)

[0119] (twenty three)

[0120] in, The voltage across the intermediate DC capacitor in the AC-DC-AC converter. The modulation signal for the grid-side converter. This refers to the current flowing from the grid-side filter circuit towards the power grid. The modulation signal for the rotor-side converter. Where is the instantaneous current of the rotor winding, and C is the DC bus capacitance.

[0121] The time-varying modulation signal is given by equations (24) and (25).

[0122] (twenty four)

[0123] (25)

[0124] In this context, the subscript ref indicates a reference value. This refers to the output voltage of the rotor-side converter. This refers to the output voltage of the grid-side converter. , These represent the modulation ratio and phase shift angle of the positive sequence modulation signal of the grid-side converter, respectively. , These represent the modulation ratio and phase shift angle of the negative sequence modulation signal of the grid-side converter, respectively. , These represent the modulation ratio and phase shift angle of the negative sequence modulation signal in the rotor-side converter, respectively. , These are the modulation ratio and phase shift angle of the positive sequence modulation signal of the rotor-side converter, respectively.

[0125] The original model of the grid-connected filter circuit is subjected to dq-sequence dynamic phasor transformation to output the dynamic phasor time-varying model of the grid-connected filter circuit. In this model, the DC capacitor voltage retains the DC and second harmonic components, and the grid-side voltage, grid-side current, and GSC modulation signal retain the positive and negative sequence fundamental frequency components, as shown in Equation (26).

[0126] (26)

[0127] in, The voltage across the intermediate DC capacitor in the AC-DC-AC converter. The modulation signal for the grid-side converter. For grid-side filter inductors, For grid-side filter resistors, This refers to the three-phase AC voltage on the grid side. Let t be the fundamental angular frequency of the power grid, and t be the time variable.

[0128] It should be noted that the original model of the entire electrical system was... dq After processing using the sequence dynamic phasor modeling method, the periodic time-varying characteristics are greatly reduced, while the time-invariant characteristics are significantly enhanced. However, due to the consideration of the generator's electromagnetic torque... DC capacitor voltage u dc The second harmonic component in the model results in a model that is still a nonlinear periodic time-varying model overall.

[0129] S3: The nonlinear periodic time-varying dynamic model of the mechanical system, the nonlinear periodic time-varying dynamic model of the control system, and the simplified nonlinear periodic time-varying dynamic model of the electrical system are linearized on the steady-state periodic trajectory, and the algebraic variables are integrated and eliminated to obtain the 47th order linear periodic time-varying small-signal model of the doubly-fed wind power grid-connected system.

[0130] The nonlinear periodic time-varying dynamic model of the mechanical system (Equation (1)-(2)), the nonlinear periodic time-varying dynamic model of the control system (Equation (12)-(17)), and the simplified nonlinear periodic time-varying dynamic model of the electrical system (Equation (18)-(26)) are directly linearized on the steady-state periodic trajectory to obtain the corresponding linear time-periodic (LTP) model.

[0131] By integrating the mechanical, electrical and control system LTP model and eliminating algebraic variables, the generalized 47th order LTP small-signal model of the DFIG grid-connected system is obtained, as shown in Equation (27).

[0132] (27)

[0133] in, Indicates the amount of change; For state variables, For input variables, The state matrix, The input matrix; , , , As shown in equations (28), (29), (30), and (31).

[0134] (28)

[0135] (29)

[0136] (30)

[0137] Wherein, submatrix It is a block partitioning of the system state matrix in the LTP small-signal model. express about The coefficient; express about , The coefficient; express about The coefficient; express about The coefficient; express about The coefficient; express about , The coefficient; express about The coefficient; express about The coefficient; express about The coefficient; express about , The coefficient; express about The coefficient; express about The coefficient; express about coefficient, express about , coefficient, express about coefficient, express about The coefficient;

[0138] (31)

[0139] in, express and The first four elements are about coefficient, express The sum of the last four elements about coefficient, express and about The coefficient.

[0140] The numbers in the parentheses indicate the size of the matrix. Let represent a 12×12 matrix of all zeros, and:

[0141] ,

[0142] ,

[0143] Table 1 lists the electrical parameters, control parameters, and wind turbine parameters of the DFIG grid-connected test system. The grid rated voltage is 690V and the frequency is 50Hz. The system is built using Matlab / Simulink. Figure 1 The electromagnetic transient simulation model of the DFIG grid-connected system is shown, and it is also based on the small-signal model shown in Matlab encapsulation (27).

[0144] Table 1

[0145]

[0146] According to GBT15543-2008, the simulated AC system asymmetrical operating condition, i.e., the negative sequence voltage imbalance does not exceed 4% during normal grid operation, is taken as 27.6V for the AC system. Assume a wind speed of 11m / s during steady-state operation. At this time, the DFIG generator system is in the maximum power point tracking (MPPT) operating region, i.e., the pitch angle is 0, and the DFIG operates in a subsynchronous state.

[0147] The accuracy and effectiveness of this invention are verified from two perspectives. First, a small disturbance is introduced, and the consistency between the simulation results of the electromagnetic transient model and the small-signal model of this invention is compared. Second, a sudden change in control parameters is introduced, causing the system to become unstable due to a small disturbance. At this time, the dominant oscillation mode of the system is fully excited, and the consistency between the oscillation frequency shown by the time-domain simulation curve and the oscillation frequency obtained by the small-signal model analysis is compared.

[0148] Figure 9 To verify the small-signal model of the AC system under asymmetrical operating conditions with varying wind speed, (a), (b), (c), and (d) represent the simulation results of electromagnetic torque, rotor speed, positive-sequence d-axis component of stator current, and positive-sequence d-axis component of rotor current, respectively. Figure 10 To verify the small-signal model of DC voltage step change under asymmetrical operating conditions of the AC system, (a), (b), (c), and (d) represent the simulation results of DC voltage, GSC output active power, positive-sequence d-axis component of grid-side current, and positive-sequence q-axis component of grid-side current, respectively. Reference values ​​of DC voltage are given for wind speed changes from 11 m / s to 10 m / s at 7 s and at 8 s, respectively. u dcref Simulation results of the electromagnetic transient model (green solid line) and the small-signal model (black solid line) are compared when the voltage jumps from 1800V to 1710V. It can be seen that the dynamic responses of the two models agree well, verifying the effectiveness and correctness of the small-signal model.

[0149] Further, set k p7 The value jumps from 0.005 to 0.01 at 5 seconds. The simulation results of the electromagnetic transient model are as follows: Figure 11 As shown. It can be seen that the rotor has a negative sequence. d The shaft current exhibits oscillation and divergence, making the system unstable. The oscillation period is 0.055625s, corresponding to an oscillation frequency of 18Hz.

[0150] Other parameters remain unchanged, when k p7 When ω = 0.01, the characteristic indices and oscillation frequencies corresponding to all oscillation modes of the system calculated by the small-signal model are shown in Table 2. From Table 2, it can be seen that... k p7When the coefficient of performance (COP) is 0.01, the real part of the characteristic exponent of oscillation mode 5 of the system is positive, which is the dominant mode leading to system instability. The oscillation frequency corresponding to mode 5 is 18.12 Hz, which is consistent with the frequency obtained from the time-domain simulation above.

[0151] Table 2

[0152]

[0153] Note: In the table, the real part of the characteristic exponent of the LTP model represents the system damping and determines the system stability. The value of its imaginary part is not unique and differs from each other by 2kπ (k=±1,±2…), causing the frequency represented by the imaginary part to be an integer multiple of the actual oscillation frequency or the fundamental frequency. This is an inherent characteristic of the LTP model.

[0154] Example 2:

[0155] This embodiment provides an electronic device for a small-signal modeling method of a doubly-fed induction generator (DFIG) wind power grid-connected system under AC asymmetric operating conditions. The device includes a memory and a processor. The memory contains a program for the small-signal modeling method of the DFIG wind power grid-connected system under AC asymmetric operating conditions. When executed by the processor, this program implements the steps of the small-signal modeling method of the DFIG wind power grid-connected system under AC asymmetric operating conditions as described in Embodiment 1. Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention and are not intended to limit the implementation of the present invention. For those skilled in the art, other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively describe all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A small-signal modeling method for a doubly-fed induction generator (DFIG) wind power grid-connected system under AC asymmetric operating conditions, characterized in that, Includes the following steps: Establish nonlinear periodic time-varying dynamic models of mechanical systems, original nonlinear periodic time-varying dynamic models of electrical systems, and nonlinear periodic time-varying dynamic models of control systems; The nonlinear periodic time-varying dynamic model of the control system includes time-domain models of the phase-locked loop and phase sequence separation element, rotor-side control model, and grid-connected side control model, which are established based on the following physical relationships: A time-domain model of the phase-locked loop and phase sequence separation element is established using a phase-locked loop and a complex filter. A rotor-side control model is established using a cascaded proportional-integral regulator control strategy for the power outer loop and current inner loop of the rotor-side converter, and a negative-sequence current vector control strategy. A grid-connected control model is established using a cascaded proportional-integral regulator control strategy for the outer voltage loop and inner current loop of the grid-connected converter, and a negative-sequence current vector control strategy. The original nonlinear periodic time-varying dynamic model of the electrical system is subjected to dq-order dynamic phasor transformation, and the dominant frequency components of key variables are retained to obtain a simplified nonlinear periodic time-varying dynamic model of the electrical system. When performing dq-sequence dynamic phasor transformation on the original nonlinear periodic time-varying dynamic model of the induction generator, the electromagnetic torque retains DC and second harmonic components, the stator voltage and current retain positive and negative sequence fundamental frequency components, and the rotor voltage and current retain positive sequence s harmonic and negative sequence (2-s) harmonic components, where s is the slip. When performing dq-sequence dynamic phasor transformation on the original AC-DC-AC power converter model, the DC voltage retains the DC and second harmonic components, the grid-side current and the grid-connected converter modulation signal retain the positive and negative fundamental frequency components, and the rotor current and the rotor-side converter modulation signal retain the positive s harmonic and negative (2-s) harmonic components. When performing dq-sequence dynamic phasor transformation on the original model of the grid-connected filter circuit, the DC voltage retains the DC and second harmonic components, while the grid-side voltage, grid-side current, and GSC modulation signal retain the positive and negative sequence fundamental frequency components. The nonlinear periodic time-varying dynamic model of the mechanical system, the nonlinear periodic time-varying dynamic model of the control system, and the simplified nonlinear periodic time-varying dynamic model of the electrical system are linearized on the steady-state periodic trajectory. The algebraic variables are then integrated and eliminated to obtain the linear periodic time-varying small-signal model of the doubly-fed wind power grid-connected system.

2. The small-signal modeling method for a doubly-fed induction generator (DFIG) wind power grid-connected system under AC asymmetric operating conditions according to claim 1, characterized in that, The original nonlinear periodic time-varying dynamic model of the electrical system includes an induction generator model, an AC-DC-AC power converter model, and a grid-connected filter circuit model, which are established based on the following physical relationships: A primitive nonlinear periodic time-varying dynamic model of an induction generator is established using the three-phase voltage balance equation, flux linkage equation, and electromagnetic torque equation of the stator / rotor of the induction generator. The original model of the AC-DC-AC power converter is established using the DC-side power balance equation, the converter modulation signal expression, and the relationship between the AC output voltage and DC voltage of the converter. The original model of the grid-connected filter circuit is established using the current-voltage relationship equation of the grid-connected filter circuit.

3. The small-signal modeling method for a doubly-fed induction generator (DFIG) wind power grid-connected system under AC asymmetric operating conditions according to claim 2, characterized in that, The simplified nonlinear periodic time-varying dynamic model of the electrical system includes: a dynamic phasor model of the induction generator, a dynamic phasor model of the converter, and a dynamic phasor model of the grid-connected filter circuit. The original nonlinear periodic time-varying dynamic model of the electrical system is subjected to a dq-sequence dynamic phasor transformation to obtain the simplified nonlinear periodic time-varying dynamic model of the electrical system, including the following steps: The original nonlinear periodic time-varying dynamic model of the induction generator is subjected to dq-sequence dynamic phasor transformation to output the dynamic phasor model of the induction generator. The original AC-DC-AC power converter model is subjected to dq-sequence dynamic phasor transformation to output the converter dynamic phasor model. The original model of the grid-connected filter circuit is subjected to dq-sequence dynamic phasor transformation to output the dynamic phasor model of the grid-connected filter circuit.

4. The small-signal modeling method for a doubly-fed wind power grid-connected system under AC asymmetric operating conditions according to claim 2, characterized in that, The converter modulation signal expression includes the modulation signal expression of the rotor-side converter and the modulation signal expression of the grid-connected converter.

5. The small-signal modeling method for a doubly-fed induction generator (DFIG) wind power grid-connected system under AC asymmetric operating conditions according to claim 1, characterized in that, The phase-locked loop is a first-order proportional-integral (PII) phase-locked loop.

6. The small-signal modeling method for a doubly-fed induction generator (DFIG) wind power grid-connected system under AC asymmetric operating conditions according to claim 1, characterized in that, The complex filter is a multi-complex filter.

7. The small-signal modeling method for a doubly-fed induction generator (DFIG) wind power grid-connected system under AC asymmetric operating conditions according to claim 1, characterized in that, The linear periodic time-varying small signal model is a 47th-order state-space model.

8. An electronic device for modeling small-signal models of a doubly-fed wind power grid-connected system under AC asymmetric operating conditions, characterized in that, The device includes a memory and a processor. The memory includes a program for modeling a small-signal model of a doubly-fed wind power grid-connected system under AC asymmetric operating conditions. When the processor executes the program for modeling a small-signal model of a doubly-fed wind power grid-connected system under AC asymmetric operating conditions, it implements the steps of the small-signal model modeling method for a doubly-fed wind power grid-connected system under AC asymmetric operating conditions as described in any one of claims 1 to 7.

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