Eigenvalue analysis method for grid-connected characteristics of doubly-fed wind farm considering unbalanced grid voltage

Abstract

The application relates to a double-fed wind farm grid-connection eigenvalue analysis method considering unbalanced grid voltage, and dynamic mathematical models of each element of a system are established; a system balance point is obtained based on a frequency shift method; the dynamic mathematical models of each element of the system are linearized to obtain corresponding linearized continuous state space models; each element continuous state space model is discretized based on a trapezoidal integration rule, according to the connection characteristics of each element in the system and the continuous state space model characteristics of each element, the system elements are divided into single-port elements and double-port elements, and the discrete state space models of different port elements with a unified description form and discrete equivalent circuits thereof are obtained; a full-system discrete state space model is constructed based on a node analysis method, and a system discrete state matrix is obtained. The double-frequency component introduced when a balance point is obtained by adopting a Park transformation is avoided; the discrete state space model of the double-fed wind turbine grid-connection system is established, and the selection process of system state variables is simplified.

Description

Technical Field

[0001] This invention belongs to the field of power system stability analysis technology, specifically involving a method for analyzing the grid-connected characteristic values ​​of doubly fed wind farms that considers unbalanced grid voltage. Background Technology

[0002] With the large-scale development of new energy sources and the rapid construction of DC transmission projects, the trend of "high-efficiency and high-power" development in the power system is becoming increasingly apparent, and the small-disturbance stability problem of the power system is becoming increasingly prominent. Meanwhile, areas rich in wind energy resources are often located in remote areas, requiring wind farms to be connected to the main grid via long transmission lines. Factors such as line impedance and grid faults can lead to grid voltage imbalances, which in turn cause imbalances in the stator and rotor currents of the doubly-fed induction generator (DFIG), thus affecting the operating performance and safety of the DFIG. Therefore, it is necessary to study the small-disturbance stability problem of DFIG grid-connected systems under grid voltage imbalance conditions. While eigenvalue analysis is commonly used for small-disturbance stability analysis of power systems, the Park transform is used to find the system equilibrium point. However, when the system is a three-phase unbalanced system, the Park transform is no longer applicable, necessitating the search for new methods to determine the system equilibrium point.

[0003] Therefore, at present, it is necessary to design a method, system, and storage medium for analyzing the grid-connected characteristic values ​​of doubly-fed wind farms that takes into account unbalanced grid voltage in order to solve the above problems. Summary of the Invention

[0004] The purpose of this invention is to provide a method, system, and storage medium for analyzing the grid-connected characteristic values ​​of doubly-fed wind farms considering unbalanced grid voltage. This invention addresses the technical problems existing in the prior art. By employing a frequency shift transformation method, the equilibrium point of the doubly-fed wind farm grid-connected system under unbalanced grid voltage conditions is obtained. Furthermore, a discrete state-space model of the doubly-fed wind farm grid-connected system is constructed, avoiding the difficulty in selecting state variables during continuous state-space modeling.

[0005] To achieve the above objectives, the technical solution of the present invention is as follows:

[0006] A method for analyzing the grid-connected eigenvalues ​​of doubly-fed induction generator (DFIG) wind farms considering unbalanced grid voltage includes the following steps:

[0007] S1: Based on the topology of the doubly fed wind farm grid-connected system, establish dynamic mathematical models for each component;

[0008] S2: The system equilibrium point is obtained based on frequency shift transform. The system model is linearized at the equilibrium point to establish a linearized continuous state-space model.

[0009] S3: Based on the connection characteristics of each component in the system and the characteristics of its continuous state space model, the system components are divided into single-port components and two-port components. The continuous state space model of each component is discretized using the trapezoidal integration rule, and the discrete state space model of different port components with a unified description form and its discrete equivalent circuit are obtained.

[0010] S4: Based on the discrete state-space model of each component, the nodal method is used to construct the discrete state-space model of the entire system;

[0011] S5: Obtain the discrete state matrix, and obtain the continuous eigenvalues ​​based on the relationship between discrete and continuous eigenvalues, and perform eigenvalue analysis.

[0012] Furthermore, step S1 is detailed as follows:

[0013] Based on the structure of the doubly fed wind turbine connected to the grid via series compensation, the system components are divided into single-port components and dual-port components according to their connection relationship with the network. In the system, single-port components include the doubly fed wind turbine and the series compensation capacitor, while dual-port components include the transformer and the AC transmission line.

[0014] Furthermore, step S2 is detailed as follows:

[0015] Establish continuous state-space models for single-port and dual-port components in the dq synchronous rotating coordinate system, respectively;

[0016] (1) Continuous state space modeling of doubly fed wind turbines;

[0017] The dynamic mathematical model of the doubly-fed induction generator (DFIG) includes the equivalent model of the dual-mass shaft system, the DFIG induction motor model, the filter model, and the converter and its control system model. The dynamic mathematical models of each module are as follows:

[0018] 1) Shaft system model:

[0019]

[0020] Among them, H t H is the inertial constant of the wind turbine. g Let ω be the generator rotor inertia constant. t ω is the rotational speed of the fan shaft system. r Rotor speed, T m T represents the mechanical torque of the wind turbine. e K represents the electromagnetic torque of the fan. s θ is the shaft system stiffness coefficient. s For the angular displacement of the shaft system, θ r B is the rotor angular displacement. s This refers to the shaft system damping coefficient;

[0021] 2) Generator model:

[0022] Following conventional practices for electric motors, neglecting magnetic saturation and core losses, the rotor-side windings are converted to the stator-side, resulting in equal turns per phase winding. The dynamic mathematical models of the doubly-fed induction generator in the three-phase natural stationary ABC / abc coordinate system are expressed as follows:

[0023] ① Three-phase stator winding voltage equation

[0024]

[0025] Among them, u sA u sB u sC These are the instantaneous voltages of the three phases A, B, and C of the stator, i sA i sB i sC These are the instantaneous currents of the three phases A, B, and C of the stator, respectively, ψ sA ψ sB ψ sC These are the stator three-phase winding flux linkages (A, B, C), and R. s Constant voltage for stator windings;

[0026] Taking the voltage equation of stator phase A winding as an example, the method of finding the equilibrium point based on frequency shift transformation is explained. First, the imaginary part of the signal is constructed, as shown in equation (3).

[0027]

[0028] The voltage equation is expressed in complex form as shown in equation (4).

[0029]

[0030] In the formula, ψ sA-s(t) Represents a complex signal;

[0031] Shift the spectrum of the above complex signal to the left by ω s The complex envelope signal with its frequency concentrated around 0 is obtained, as shown in equation (5);

[0032]

[0033] Separating the real and imaginary parts of the above equation, we can express it as follows:

[0034]

[0035] In the formula, the subscript E represents the signal after frequency shift transformation, the subscript Re represents the real part of the complex signal, and the subscript Im represents the imaginary part of the complex signal;

[0036] Similarly, the equation after the BC phase shift transformation can be obtained, expressed as follows:

[0037]

[0038] ② Three-phase rotor winding voltage equation

[0039]

[0040] Among them, u ra u rb u rc These are the instantaneous voltages of the rotor's three phases A, B, and C, respectively, i ra i rb i rc These are the instantaneous currents of the rotor's three phases A, B, and C, respectively, ψ ra ψ rb ψ rc These are the flux linkages of the rotor's three-phase windings ABC, and R. r Set constant voltage for the rotor winding;

[0041] Performing a frequency shift transformation on equation (9), we obtain the rotor voltage equation after the frequency shift transformation as follows:

[0042]

[0043] ③ Stator and rotor flux linkage equations

[0044] The stator and rotor flux linkage equations in the three-phase naturally stationary ABC / abc coordinate system are expressed as follows:

[0045]

[0046] In the formula ψ s =[ψ sA ,ψ sB ,ψ sC ], ψ r =[ψ ra ,ψ rb ,ψ rc ], L ss L is the inductance matrix between the stator windings. rr L is the inductance matrix between the rotor windings. sr and L rs Let L be the mutual inductance matrix between the stator winding and the rotor winding, and L... sr =L rs T ;

[0047] Similarly, by performing a frequency shift transformation on equation (13), we obtain...

[0048]

[0049] Combining equations (6)-(8), (10)-(12), and (14), the doubly-fed synchronous induction generator model with stator current and rotor current as state variables is obtained as follows:

[0050]

[0051] The coefficient matrix is ​​expressed as follows:

[0052]

[0053] 3) Controller model:

[0054] Both the rotor-side controller and the grid-side controller adopt vector control based on stator voltage orientation. The controller uses a dq synchronous rotating coordinate system, and the input signal is a real number signal. Therefore, the controller input signal needs to be further processed. At the same time, positive and negative sequence controllers for RSC and GSC are designed respectively to suppress negative sequence components.

[0055] With any complex signal x i_sfa For example, i = a, b, c, this illustrates the implementation of the electrical-control signal interface;

[0056] First, the positive and negative sequence signals are separated. Based on the symmetric component method, the following is obtained:

[0057]

[0058] Where x1, x2, and x3 represent the positive-sequence, negative-sequence, and zero-sequence signals, respectively.

[0059] Performing Park transforms on the positive and negative sequence signals respectively yields the positive and negative sequence signals in the dq coordinate system, represented as follows:

[0060]

[0061] At this point, the conversion from complex signals in the electrical section to real signals in the controller section can be realized; next, the dynamic mathematical models of RSC and GSC will be constructed respectively.

[0062] ①RSC dynamic mathematical model:

[0063] The state equation of RSC is:

[0064]

[0065] The algebraic equation is:

[0066]

[0067] This is converted into a complex signal with the same descriptive form as the generator's electrical components; the construction method for the complex signal is the same as that for the complex signal in the electrical components; therefore, the controller output signal is represented as...

[0068]

[0069] Among them, u ar_E u br_E u cr_E These represent the three-phase rotor voltages after frequency shift, u ar_ERe u br_ERe u cr_ERe Let u and u represent the real parts of the rotor phase voltages after frequency shifting. ar_EIm u br_EIm u cr_EIm These represent the imaginary parts of the rotor phase voltages after frequency shifting;

[0070] ②GSC Dynamic Mathematical Model:

[0071] The state equation and algebraic equation of GSC are expressed as follows:

[0072]

[0073] ③ DC capacitor model:

[0074] According to the law of conservation of energy, the power balance equation for a DC capacitor is as follows:

[0075]

[0076] Among them, C dc For DC capacitor, u dc P is the DC capacitor voltage. g P represents the active power on the grid side. r This refers to the active power on the rotor side.

[0077] 4) Filter model:

[0078] Dynamic mathematical model of filter in three-phase natural static ABC coordinate system

[0079]

[0080] The filter model after frequency shift transformation is expressed as follows:

[0081]

[0082] Linearize equations (1), (15), (19), (22), (23) and (25) at the equilibrium point to obtain the continuous state space model of the doubly fed wind turbine under the condition of grid voltage imbalance, as shown in equation (26).

[0083]

[0084] Where, x DFIG =[x M x G x DCx RSC x f x GSC ] T x M x is the state variable of the shaft system. G x is the state variable of the doubly-fed asynchronous motor. DC x is the state variable of the DC capacitor. RSC x is the state variable of the rotor-side controller. f Let x be the filter state variable. GSC For the state variables of the network-side controller; u DFIG Let i be the input vector. DFIG A is the output vector; DFIG1 B DFIG1 C DFIG1 D DFIG1 These are the coefficient matrices;

[0085] (2) Continuous state-space modeling of transmission lines:

[0086] Dynamic mathematical model of AC lines in three-phase natural static ABC coordinate system

[0087]

[0088] The AC line model after frequency shift transformation is represented as follows:

[0089]

[0090] Linearizing equation (28) at the equilibrium point yields a continuous state-space model of the AC transmission line, expressed as follows:

[0091]

[0092] Where, x l For state variables, u l1 u l2 Let i be the input vector. l For the output vector, A l B l1 B l2 C l D l1 D l2 These are the coefficient matrices;

[0093] (3) Continuous state-space modeling of series compensation capacitors:

[0094] Dynamic mathematical model of AC lines in three-phase natural static ABC coordinate system

[0095]

[0096] The AC line model after frequency shift transformation is represented as follows:

[0097]

[0098] Linearizing equation (31) at the equilibrium point yields the continuous state-space model of the series compensation capacitor, as shown in equation (32).

[0099]

[0100] Where x c For the state variable of the series capacitor, u c Let y be the input vector. c For the output vector, A c1 B c1 C c1 D c1 These are the coefficient matrices.

[0101] Furthermore, step S3 is as follows:

[0102] Based on the connection method of each component in the doubly fed wind turbine grid-connected system, the system components are divided into single-port components and dual-port components. Among them, the single-port components are the doubly fed wind turbine and the series compensation capacitor, and the dual-port components are the AC transmission lines.

[0103] The discrete state-space models of single-port and dual-port components are established below respectively;

[0104] (1) Discrete state-space modeling of single-port components:

[0105] Based on the trapezoidal integral rule, the continuous state space model of the doubly fed wind turbine shown in Equation (26) and the continuous state space model of the series compensation capacitor shown in Equation (32) are linearized to obtain the discrete state space models of the doubly fed wind turbine and the series compensation capacitor as shown in Equation (33) and Equation (34), respectively.

[0106]

[0107] Where, the subscript t represents the quantity at the current time, the subscript represents the quantity at the previous time t-Δt, Δt is the integration step size, and i hDFIG(t) A represents the historical current term related to the previous time step; DFIGd B DFIGd C DFIGd D DFIGd These are the coefficient matrices of the discrete state-space model of the doubly-fed induction generator (DFIG), i hDFIG(t-Δt) A is a state variable; cd B cd C cd D cd These are the coefficient matrices of the discrete state-space model of the series-complementary capacitor, i. hC(t-Δt)For state variables;

[0108] Based on the discrete state-space model of the single-port element shown in equations (33) and (34), its discrete equivalent circuit is obtained.

[0109] (2) Discrete state-space modeling of two-port components:

[0110] Similarly, based on the trapezoidal integral rule, the continuous state-space model of the AC transmission line shown in the equation is discretized to obtain its discrete state-space model, expressed as follows:

[0111]

[0112] Among them, A ld B ld C ld D ld These are the coefficient matrices of the discrete state-space model of an AC transmission line, i hl(t-Δt) For state variables;

[0113] Based on the discrete state-space model of AC transmission lines (35), the discrete equivalent circuit of two-port components is obtained.

[0114] Furthermore, step S4 is detailed as follows:

[0115] Based on the nodal analysis method, the discrete state-space model of the system is obtained from the discrete state-space models of each component.

[0116] As shown in equation (36);

[0117]

[0118] Wherein, coefficient matrix A d B d C d D d The expressions are respectively

[0119]

[0120] The discrete equivalent circuit of the doubly fed wind farm grid-connected system is obtained.

[0121] Furthermore, step S5 is detailed as follows:

[0122] Based on the discrete-state empty model of the system, the discrete-state matrix of the system is obtained; the calculation method is as follows:

[0123] Based on the discrete equivalent circuit, the system branch-node correlation matrix is ​​obtained, as shown in equation (37);

[0124]

[0125] Where I is the identity matrix;

[0126] According to the discrete state-space model, the coefficient matrix D of the system's discrete state-space model is... d The equivalent conductance of each branch element is given by [formula missing]. The node conductance is expressed as [formula missing].

[0127] G = L T D d L (34)

[0128] The branch voltage is represented by the branch-node correlation matrix as follows:

[0129] u (t-Δt) =LU node(t-Δt) (39)

[0130] Based on the relationship between node voltage and node current, the node voltage is expressed as:

[0131] U node(t-Δt) =G -1 L T C d i h(t-Δt) (40)

[0132] Combining equations (12)-(15), eliminating intermediate variables, the discrete state matrix of the system is obtained as shown in equation (41);

[0133] A d_sys =A d +B d LG -1 L T C d (41)

[0134] When using the trapezoidal integral rule for discretization, the relationship between discrete eigenvalues ​​and continuous eigenvalues ​​is expressed as follows:

[0135]

[0136] Where Δt is the distance from the walk, λ i For continuous eigenvalues, z i These are discrete eigenvalues;

[0137] Therefore, by solving the discrete state matrix A d_sys The discrete eigenvalues ​​of the system are obtained, and the continuous eigenvalues ​​of the system are obtained according to the relationship between the discrete eigenvalues ​​and continuous eigenvalues ​​shown in equation (42).

[0138] The doubly-fed induction generator (DFIG) wind farm grid connection characteristic value analysis system considering unbalanced grid voltage adopts the above-mentioned method for analyzing the grid connection characteristic value of DFIG wind farms.

[0139] A storage medium storing a computer program, which, when run, executes the doubly fed wind farm grid-connected characteristic value analysis method considering unbalanced grid voltage as described above.

[0140] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0141] This invention employs frequency shift transformation to determine the equilibrium point of a doubly-fed induction generator (DFIG) wind farm grid-connected system under grid voltage imbalance conditions, avoiding the second harmonic component introduced when using Park transformation. A discrete state-space model of the DFIG wind turbine grid-connected system is established, simplifying the selection process of system state variables. Attached Figure Description

[0142] Figure 1 This is a block diagram of a doubly fed wind farm grid-connected system according to a specific embodiment of the present invention;

[0143] Figure 2 This is a block diagram of the RSC control of a doubly fed fan according to a specific embodiment of the present invention;

[0144] Figure 3 This is a block diagram of the GSC control system for a doubly fed wind turbine according to a specific embodiment of the present invention;

[0145] Figure 4 This is a discrete equivalent circuit of a single-port element according to a specific embodiment of the present invention;

[0146] Figure 5 This is a discrete equivalent circuit of a two-port element according to a specific embodiment of the present invention;

[0147] Figure 6 This is a schematic diagram of the discrete equivalent circuit of a system according to a specific embodiment of the present invention. Detailed Implementation

[0148] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only for explaining the invention and are not intended to limit the invention; that is, the described embodiments are merely some embodiments of the invention, and not all embodiments. The components of the embodiments of the invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0149] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention. It should be noted that relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations.

[0150] Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0151] Example:

[0152] A method for eigenvalue analysis of a doubly fed wind farm grid-connected system considering unbalanced grid voltage.

[0153] Includes the following steps:

[0154] S1. According to Figure 1 The doubly fed wind turbine connected to the grid via series compensation system shown in the figure divides the system components into single-port components and dual-port components according to their connection relationship with the network. In this system, the single-port components include the doubly fed wind turbine and the series compensation capacitor, while the dual-port components include the transformer and the AC transmission line.

[0155] S2. Establish continuous state space models for single-port and dual-port components in the dq synchronous rotating coordinate system, respectively.

[0156] (1) Continuous state space modeling of doubly fed wind turbine

[0157] The dynamic mathematical model of the doubly-fed induction generator (DFIG) includes the equivalent model of the dual-mass shaft system, the DFIG induction motor model, the filter model, and the converter and its control system model. The dynamic mathematical models of each module are as follows:

[0158] 1) Shaft system model:

[0159]

[0160] Among them, H t H is the inertial constant of the wind turbine. g Let ω be the generator rotor inertia constant.t ω is the rotational speed of the fan shaft system. r Rotor speed, T m T represents the mechanical torque of the wind turbine. e K represents the electromagnetic torque of the fan. s θ is the shaft system stiffness coefficient. s For the angular displacement of the shaft system, θ r B is the rotor angular displacement. s is the shaft damping coefficient.

[0161] 2) Generator Model

[0162] Following conventional practices for electric motors, neglecting magnetic saturation and core losses, the rotor-side windings are converted to the stator-side windings, resulting in equal turns per phase. The dynamic mathematical models of the doubly-fed induction generator in the three-phase natural stationary ABC / abc coordinate system are expressed as follows:

[0163] ① Three-phase stator winding voltage equation

[0164]

[0165] Among them, u sA u sB u sC These are the instantaneous voltages of the three phases A, B, and C of the stator, i sA i sB i sC These are the instantaneous currents of the three phases A, B, and C of the stator, respectively, ψ sA ψ sB ψ sC These are the stator three-phase winding flux linkages (A, B, C), and R. s To provide constant voltage for the stator windings.

[0166] The method for finding the equilibrium point based on frequency shift transformation is illustrated using the voltage equation of the stator A-phase winding as an example. First, the imaginary part of the signal is constructed, as shown in equation (3).

[0167]

[0168] The voltage equation is expressed in complex form as shown in equation (4).

[0169]

[0170] In the formula, ψ sA-s(t) It represents a complex signal.

[0171] Shift the spectrum of the above complex signal to the left by ω s The complex envelope signal with its frequency concentrated around 0 is obtained, as shown in equation (5).

[0172]

[0173] Separating the real and imaginary parts of the above equation, it can be expressed as:

[0174]

[0175] In the formula, the subscript E represents the signal after frequency shift transformation, the subscript Re represents the real part of the complex signal, and the subscript Im represents the imaginary part of the complex signal.

[0176] Similarly, the equation after the BC phase-shift frequency transformation can be obtained, which can be expressed as:

[0177]

[0178] ② Three-phase rotor winding voltage equation

[0179]

[0180] Among them, u ra u rb u rc These are the instantaneous voltages of the rotor's three phases A, B, and C, respectively, i ra i rb i rc These are the instantaneous currents of the rotor's three phases A, B, and C, respectively, ψ ra ψ rb ψ rc These are the flux linkages of the rotor's three-phase windings ABC, and R. r Set constant voltage for the rotor winding.

[0181] Performing a frequency shift transformation on equation (9), we obtain the rotor voltage equation after the frequency shift transformation as follows:

[0182]

[0183] ③ Stator and rotor flux linkage equations

[0184] The stator and rotor flux linkage equations in the three-phase naturally stationary ABC / abc coordinate system can be expressed as follows:

[0185]

[0186] In the formula ψ s =[ψ sA ,ψ sB ,ψ sC ], ψ r =[ψ ra ,ψ rb ,ψ rc ], L ss L is the inductance matrix between the stator windings. rr L is the inductance matrix between the rotor windings. sr and L rsLet L be the mutual inductance matrix between the stator winding and the rotor winding, and L... sr =L rs T .

[0187] Similarly, by performing a frequency shift transformation on equation (13), we obtain...

[0188]

[0189] Combining equations (6)-(8), (10)-(12), and (14), the doubly-fed synchronous induction generator model with stator current and rotor current as state variables is obtained as follows:

[0190]

[0191] The coefficient matrix is ​​expressed as follows:

[0192]

[0193] 3) Controller Model

[0194] Both the rotor-side controller (RSC) and the grid-side controller (GSC) employ stator voltage-oriented vector control. Unlike the generator's electrical components, the controllers use a dq synchronous rotating coordinate system, and the input signals are real numbers. Therefore, further processing of the controller input signals is required. Furthermore, due to the three-phase voltage imbalance in the grid, separate positive and negative sequence controllers need to be designed for both the RSC and GSC to suppress the negative sequence component.

[0195] With any complex signal x i_sfa Taking (i = a, b, c) as an example, the implementation of the electrical-control signal interface is explained. First, the positive and negative sequence signals are separated. Based on the symmetrical component method, the following is obtained:

[0196]

[0197] Where x1, x2, and x3 represent the positive-sequence, negative-sequence, and zero-sequence signals, respectively.

[0198] Furthermore, by performing Park transform on the positive and negative sequence signals respectively, we obtain the positive and negative sequence signals in the dq coordinate system, which can be expressed as follows:

[0199]

[0200] This completes the conversion from complex signals in the electrical section to real signals in the controller section. Next, the dynamic mathematical models for RSC and GSC will be constructed respectively.

[0201] ①RSC Dynamic Mathematical Model

[0202] according to Figure 2 The RSC control block diagram shown yields the following state equation for RSC:

[0203]

[0204] according to Figure 2 The control block diagram shown further yields the algebraic equation as follows:

[0205]

[0206] Since the controller output signal is a real number signal, it needs to be converted into a complex number signal with the same descriptive form as the generator's electrical components. The construction method for the complex number signal is the same as that for the complex number signals in the electrical components. Therefore, the controller output signal can be further represented as...

[0207]

[0208] Among them, u ar_E u br_E u cr_E These represent the three-phase rotor voltages after frequency shift, u ar_ERe u br_ERe u cr_ERe Let u and u represent the real parts of the rotor phase voltages after frequency shifting. ar_EIm u br_EIm u cr_EIm These represent the imaginary parts of the rotor phase voltages after frequency shifting.

[0209] ②GSC Dynamic Mathematical Model

[0210] according to Figure 3 The GSC control block diagram shown can be used to express the state equations and algebraic equations of the GSC as follows:

[0211]

[0212]

[0213] ③ DC capacitor model

[0214] Neglecting converter losses, according to the law of conservation of energy, the power balance equation for the DC capacitor is as follows:

[0215]

[0216] Among them, C dc For DC capacitor, u dc P is the DC capacitor voltage. g P represents the active power on the grid side.r This refers to the active power on the rotor side.

[0217] 4) Filter Model

[0218] Dynamic mathematical model of filter in three-phase natural static ABC coordinate system

[0219]

[0220] The filter model after frequency shift transformation can be expressed as follows:

[0221]

[0222] Linearize equations (1), (15), (19), (22), (23) and (25) at the equilibrium point to obtain the continuous state-space model of the doubly fed wind turbine under the condition of grid voltage imbalance, as shown in equation (26).

[0223]

[0224] Where, x DFIG =[x M x G x DC x RSC x f x GSC ] T x M x is the state variable of the shaft system. G x is the state variable of the doubly-fed asynchronous motor. DC x is the state variable of the DC capacitor. RSC x is the state variable of the rotor-side controller. f Let x be the filter state variable. GSC For the state variables of the network-side controller; u DFIG Let i be the input vector. DFIG A is the output vector; DFIG1 B DFIG1 C DFIG1 D DFIG1 These are the coefficient matrices.

[0225] (2) Continuous state space modeling of transmission lines

[0226] Dynamic mathematical model of AC lines in three-phase natural static ABC coordinate system

[0227]

[0228] The AC line model after frequency shift transformation can be represented as follows:

[0229]

[0230] Linearizing equation (28) at the equilibrium point yields a continuous state-space model of the AC transmission line, which can be expressed as follows:

[0231]

[0232] Where, x l For state variables, u l1 u l2 Let i be the input vector. l For the output vector, A l B l1 B l2 C l D l1 D l2 These are the coefficient matrices.

[0233] (3) Continuous state-space modeling of series compensation capacitor

[0234] Dynamic mathematical model of AC lines in three-phase natural static ABC coordinate system

[0235]

[0236] The AC line model after frequency shift transformation can be represented as follows:

[0237]

[0238] Linearizing equation (31) at the equilibrium point yields the continuous state-space model of the series compensation capacitor, as shown in equation (32).

[0239]

[0240] Where x c For the state variable of the series capacitor, u c Let y be the input vector. c For the output vector, A c1 B c1 C c1 D c1 These are the coefficient matrices.

[0241] S3. Discrete state-space modeling of doubly-fed wind turbine grid-connected systems

[0242] Based on the connection method of each component in a doubly-fed induction generator (DFIG) grid-connected system, the system components can be divided into single-port components and dual-port components. Single-port components include the DFIG and its series compensation capacitor, while dual-port components are AC transmission lines. Discrete state-space models of the single-port and dual-port components are established below.

[0243] (1) Discrete state-space modeling of single-port components

[0244] Based on the trapezoidal integral rule, the continuous state space model of the doubly fed wind turbine shown in Equation (26) and the continuous state space model of the series compensation capacitor shown in Equation (32) are linearized to obtain the discrete state space models of the doubly fed wind turbine and the series compensation capacitor as shown in Equation (33) and Equation (34), respectively.

[0245]

[0246] Where, the subscript t represents the quantity at the current time, the subscript represents the quantity at the previous time t-Δt, Δt is the integration step size, and i hDFIG(t) This represents the historical current term related to the previous time step. A DFIGd B DFIGd C DFIGd D DFIGd These are the coefficient matrices of the discrete state-space model of the doubly-fed induction generator (DFIG), i hDFIG(t-Δt) For state variables. A cd B cd C cd D cd These are the coefficient matrices of the discrete state-space model of the series-complementary capacitor, i. hC(t-Δt) It is a state variable.

[0247] Based on the discrete state-space model of the single-port element shown in equations (33) and (34), its discrete equivalent circuit is obtained, as follows: Figure 4 As shown. Figure 4 in, u mdq and i mdq i represents the node voltage and node current flowing into the element, respectively. hm(t) and G m These represent the historical current source and equivalent conductance, respectively. The subscript 'm' indicates different one-port elements.

[0248] (2) Discrete state-space modeling of two-port components

[0249] Similarly, based on the trapezoidal integral rule, the continuous state-space model of the AC transmission line shown in the equation is discretized to obtain its discrete state-space model, expressed as follows:

[0250]

[0251] Among them, A ld B ld C ld D ld These are the coefficient matrices of the discrete state-space model of an AC transmission line, i hl(t-Δt) It is a state variable.

[0252] Based on the discrete state-space model of AC transmission lines according to equation (35), the discrete equivalent circuit of the two-port element is obtained, such as... Figure 5 As shown. Figure 5 in, u idq and u jdq These represent the node voltages of a two-port element, i idq and i jdq These represent the current flowing into the node of a two-port element, i and i respectively. hn(t) and G n These represent the historical current source and equivalent conductance of the two-port element, respectively. The subscript n indicates different two-port elements.

[0253] S4. Based on the node analysis method, the discrete state space model of the system can be obtained according to the discrete state space model of each component, as shown in equation (36).

[0254]

[0255] Wherein, coefficient matrix A d B d C d D d The expressions can be respectively

[0256]

[0257] Furthermore, the discrete equivalent circuit of the doubly-fed wind farm grid-connected system is obtained, such as... Figure 6 As shown.

[0258] S5. Based on the discrete-state empty model of the system, obtain the discrete-state matrix of the system. The calculation method is as follows:

[0259] according to Figure 6 The discrete equivalent circuit shown is used to obtain the system branch-node correlation matrix, as shown in equation (37).

[0260]

[0261] Where I is the identity matrix.

[0262] Furthermore, according to the discrete state-space model, the coefficient matrix D of the system's discrete state-space model is... d Given the equivalent conductance of each branch element, the node conductance can be expressed as:

[0263] G = L T D d L (34)

[0264] Furthermore, the branch voltage can be represented by the branch-node correlation matrix as follows:

[0265] u (t-Δt) =LU node(t-Δt) (39)

[0266] Furthermore, based on the relationship between node voltage and node current, the node voltage can be expressed as:

[0267] U node(t-Δt) =G -1 L T C d i h(t-Δt) (40)

[0268] Combining equations (12)-(15), the intermediate variables are eliminated, and the discrete state matrix of the system is obtained as shown in equation (41).

[0269] A d_sys =A d +B d LG -1 L T C d (41)

[0270] When using the trapezoidal integral rule for discretization, the relationship between discrete eigenvalues ​​and continuous eigenvalues ​​can be expressed as follows:

[0271]

[0272] Where Δt is the distance from the walk, λ i For continuous eigenvalues, z i These are discrete eigenvalues.

[0273] Therefore, by solving the discrete state matrix A d_sys The discrete eigenvalues ​​of the system can be obtained. Furthermore, based on the relationship between the discrete eigenvalues ​​and the continuous eigenvalues ​​shown in equation (42), the continuous eigenvalues ​​of the system can be obtained.

[0274] The above are preferred embodiments of the present invention. Any changes made to the technical solution of the present invention that do not exceed the scope of the technical solution of the present invention shall fall within the protection scope of the present invention.

Claims

1. A method for analyzing the grid-connected characteristic values ​​of a doubly-fed induction generator (DFIG) wind farm considering unbalanced grid voltage, characterized in that, Includes the following steps: S1: Based on the topology of the doubly fed wind farm grid-connected system, establish dynamic mathematical models for each component; S2: The system equilibrium point is obtained based on frequency shift transform. The system model is linearized at the equilibrium point to establish a linearized continuous state-space model. S3: Based on the connection characteristics of each component in the system and the characteristics of its continuous state space model, the system components are divided into single-port components and two-port components. The continuous state space model of each component is discretized using the trapezoidal integration rule, and discrete state space models of different port components with a unified description form and their discrete equivalent circuits are obtained. S4: Based on the discrete state-space model of each component, the nodal method is used to construct the discrete state-space model of the entire system; S5: Obtain the discrete state matrix, and obtain the continuous eigenvalues ​​based on the relationship between discrete and continuous eigenvalues, and perform eigenvalue analysis.

2. The method for analyzing the grid-connected characteristic values ​​of a doubly-fed induction generator (DFIG) wind farm considering unbalanced grid voltage as described in claim 1, characterized in that, Step S1 is as follows: Based on the structure of the doubly fed wind turbine connected to the grid via series compensation, the system components are divided into single-port components and dual-port components according to their connection relationship with the network. In the system, single-port components include the doubly fed wind turbine and the series compensation capacitor, while dual-port components include the transformer and the AC transmission line.

3. A doubly-fed induction generator (DFIG) wind farm grid-connected characteristic value analysis system considering unbalanced grid voltage, characterized in that, The grid-connected characteristic value analysis of the doubly-fed wind farm considering unbalanced grid voltage is performed using the doubly-fed wind farm grid-connected characteristic value analysis method as described in any one of claims 1-2.

4. A storage medium, characterized in that, The storage medium stores a computer program, which, when run, executes the doubly fed wind farm grid-connected characteristic value analysis method considering unbalanced grid voltage as described in any one of claims 1-2.

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