Double-fed wind power plant grid-connected characteristic value analysis method considering unbalanced power grid voltage

Abstract

The invention relates to a doubly-fed wind power plant grid-connected characteristic value analysis method considering unbalanced power grid voltage. The method comprises the following steps: establishing a dynamic mathematical model of each element of a system; solving a system balance point based on a frequency shift method; linearizing the dynamic mathematical model of each element of the system to obtain a corresponding linearized continuous state space model; discretizing the continuous state space model of each element based on a trapezoidal integral rule, and dividing the system elements into single-port elements and dual-port elements according to the connection characteristics of each element in the system and the characteristics of the continuous state space model; discrete state space models of different port elements with a unified description form and discrete equivalent circuits of the discrete state space models are obtained; a full-system discrete state space model is constructed based on a node analysis method, and a system discrete state matrix is solved. A frequency doubling component introduced when a balance point is solved by adopting Park transformation is avoided; a discrete state space model of the doubly-fed fan grid-connected system is established, and the selection process of system state variables is simplified.

Description

Technical Field

[0001] The invention belongs to the technical field of power system stability analysis, and in particular relates to a method for analyzing grid-connected characteristic values ​​of a double-fed wind farm considering unbalanced grid voltage. Background Art

[0002] With the large-scale development of new energy and the rapid construction of DC transmission projects, the "double high" development trend of the power system has become increasingly obvious, and the small disturbance stability problem of the power system has become increasingly prominent. At the same time, the areas rich in wind energy resources are located in remote areas, and wind farms need to be connected to the main grid through long transmission lines. The impedance of the line, grid faults and other factors may cause the grid voltage to be unbalanced. The unbalanced grid voltage will cause the stator and rotor current of the doubly fed wind turbine to be unbalanced, thereby affecting the operating performance and safety of the doubly fed wind turbine. Therefore, it is necessary to study the small disturbance stability problem of the doubly fed wind turbine grid-connected system under the condition of unbalanced grid voltage. When the eigenvalue analysis method is usually used for the small disturbance stability analysis of the power system, the system balance point is solved by Park transformation. However, when the system is a three-phase unbalanced system, Park transformation is no longer applicable, and new methods need to be sought to achieve the system balance point.

[0003] Therefore, at this stage, it is necessary to design a grid-connected characteristic value analysis method, system and storage medium for a doubly-fed wind farm that takes into account the unbalanced grid voltage to solve the above problems. Summary of the invention

[0004] The purpose of the present invention is to provide a method, system and storage medium for analyzing the grid-connected characteristic values ​​of a doubly-fed wind farm taking into account the unbalanced grid voltage, so as to solve the technical problems existing in the above-mentioned prior art. The method of frequency shift transformation is adopted to realize the equilibrium point acquisition of the grid-connected system of the doubly-fed wind farm under the condition of unbalanced grid voltage, and to construct a discrete state space model of the grid-connected system of the doubly-fed wind farm, thereby avoiding the difficulty in selecting state variables existing in the continuous state space modeling process.

[0005] To achieve the above object, the technical solution of the present invention is:

[0006] The method for analyzing the grid-connected characteristic value of a doubly-fed wind farm considering unbalanced grid voltage includes the following steps:

[0007] S1: Based on the topological structure of the grid-connected doubly-fed wind farm system, a dynamic mathematical model of each component is established;

[0008] S2: Obtain the system equilibrium point based on frequency shift transformation, linearize the system model at the equilibrium point, and establish a linearized continuous state space model;

[0009] S3: According to 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 dual-port components. The continuous state space model of each component is discretized using the ladder integration rule, and the discrete state space models of different port components with a unified description form and their discrete equivalent circuits are obtained;

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

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

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

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

[0014] Further, step S2 is specifically as follows:

[0015] The continuous state space modeling of single-port and dual-port components in the dq synchronous rotating coordinate system is established respectively;

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

[0017] The dynamic mathematical model of the doubly-fed wind turbine includes a double-mass shaft system equivalent model, a doubly-fed induction motor model, a filter model, and a converter and its control system model. The dynamic mathematical models of each module are as follows:

[0018] 1) Axis model:

[0019]

[0020] Among them, H t is the fan inertia constant, H g is the generator rotor inertia constant, ω t is the fan shaft speed, ω r Rotor speed, T m is the mechanical torque of the fan, T e is the electromagnetic torque of the fan, K s is the shaft stiffness coefficient, θ s is the angular displacement of the shaft system, θ r is the rotor angular displacement, B s is the shaft system damping coefficient;

[0021] 2) Generator model:

[0022] The motor convention is selected, magnetic saturation and core loss are ignored, and the rotor side winding is converted to the stator side. After conversion, the number of turns of each phase winding is equal; the dynamic mathematical model of the doubly fed induction generator in the three-phase natural stationary ABC / abc coordinate system is expressed as follows:

[0023] ①Three-phase stator winding voltage equation

[0024]

[0025] Among them, u sA 、u sB 、u sC are the stator ABC three-phase instantaneous voltages, i sA 、i sB 、i sC are the instantaneous currents of the three phases of stator ABC, ψ sA , sB , sC are the stator ABC three-phase winding flux, R s To set the voltage for stator winding;

[0026] Taking the stator A phase winding voltage equation as an example, the method of obtaining the equilibrium point based on frequency shift transformation is explained; first, the imaginary part of the signal is constructed, as shown in formula (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 , we get a complex envelope signal whose frequency is concentrated around 0, as shown in formula (5);

[0032]

[0033] Separate the real and imaginary parts of the above equation and express it as

[0034]

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

[0036] Similarly, the equation after BC phase-frequency shift transformation can be obtained, which is expressed as

[0037]

[0038] ②Three-phase rotor winding voltage equation

[0039]

[0040] Among them, u ra 、u rb 、u rc are the three-phase instantaneous voltages of the rotor, i ra 、i rb 、i rc are the three-phase instantaneous currents of the rotor ABC, ra , rb , rc They are the rotor ABC three-phase winding flux, R r To set the voltage for the rotor winding;

[0041] Perform frequency shift transformation on equation (9) to obtain the rotor voltage equation after frequency shift transformation:

[0042]

[0043] ③ Stator and rotor flux equation

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

[0045]

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

[0047] Similarly, frequency shift transformation is performed on equation (13) to 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 expression is 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 adopts dq synchronous rotating coordinate system, and the input signal is a real signal. Therefore, the controller input signal needs to be further processed. At the same time, the positive and negative sequence controllers of RSC and GSC are designed respectively to suppress the negative sequence component.

[0055] Take any complex signal x i_sfa Take for example, i = a, b, c, to illustrate the implementation of the electrical-control signal interface;

[0056] First, the positive and negative sequence signals are separated, and according to the symmetrical component method, we get

[0057]

[0058] Among them, x1, x2, and x3 represent positive sequence, negative sequence, and zero sequence signals, respectively.

[0059] Perform Park transform on the positive and negative sequence signals respectively to obtain the positive and negative sequence signals in the dq coordinate system, which are expressed as

[0060]

[0061] At this point, the conversion of the complex signal of the electrical part to the real signal of the controller part can be realized; next, the dynamic mathematical models of RSC and GSC are constructed respectively;

[0062] ①RSC dynamic mathematical model:

[0063] The state equation of RSC is

[0064]

[0065] The algebraic equation is

[0066]

[0067] Convert it into a complex signal with the same description form as the electrical part of the generator; the construction method of the complex signal is the same as the construction method of the electrical part complex signal; therefore, the controller output signal is expressed as

[0068]

[0069] Among them, u ar_E 、u br_E 、u cr_E They represent the three-phase rotor voltage after frequency shift, u ar_ERe 、u br_ERe 、u cr_ERe They represent the real part of the rotor phase voltage after frequency shift, u ar_EIm 、u br_EIm 、u cr_EIm They represent the imaginary part of the rotor phase voltage after frequency shifting respectively;

[0070] ②GSC dynamic mathematical model:

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

[0072]

[0073] ③DC capacitor model:

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

[0075]

[0076] Among them, C dc is the DC capacitance, u dc is the DC capacitor voltage, P g is the grid-side active power, P r is the active power on the rotor side;

[0077] 4) Filter model:

[0078] The dynamic mathematical model of the filter in the three-phase natural stationary ABC coordinate system is:

[0079]

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

[0081]

[0082] By linearizing equations (1), (15), (19), (22), (23) and (25) at the equilibrium point, the continuous state space model of the doubly fed wind turbine under the condition of grid voltage unbalance is obtained, as shown in equation (26);

[0083]

[0084] Among them, x DFIG =[x M x G x DCx RSC x f x GSC ] T , x M is the axis system state variable, x G is the state variable of the doubly-fed asynchronous motor, x DC is the DC capacitance state variable, x RSC is the rotor side controller state variable, x f is the filter state variable, x GSC is the state variable of the grid-side controller; u DFIG is the input vector, i DFIG is the output vector; A DFIG1 , B DFIG1 , C DFIG1 , D DFIG1 are coefficient matrices respectively;

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

[0086] The dynamic mathematical model of AC line in three-phase natural stationary ABC coordinate system is:

[0087]

[0088] The AC line model after frequency shift conversion is expressed as

[0089]

[0090] Linearizing equation (28) at the equilibrium point, we obtain the continuous state space model of the AC transmission line, which is expressed as

[0091]

[0092] Among them, x l is the state variable, u l1 、u l2 is the input vector, i l is the output vector, A l , B l1 ,B l2 ,C l , D l1 , D l2 are coefficient matrices respectively;

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

[0094] The dynamic mathematical model of AC line in three-phase natural stationary ABC coordinate system is:

[0095]

[0096] The AC line model after frequency shift conversion is expressed as

[0097]

[0098] Linearize equation (31) at the equilibrium point to obtain the continuous state space model of the series compensation capacitor, as shown in equation (32);

[0099]

[0100] where x c is the state variable of the series compensation capacitor, u c is the input vector, y c is the output vector, A c1 , B c1 , C c1 , D c1 are coefficient matrices respectively.

[0101] Furthermore, step S3 is specifically as follows:

[0102] According to the connection mode of each component in the doubly-fed wind turbine grid-connected system, the system components are divided into single-port components and double-port components, among which the single-port components are the doubly-fed wind turbine and the series compensation capacitor, and the double-port components are the AC transmission line.

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

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

[0105] Based on the trapezoidal integration 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, and the discrete state space models of the doubly fed wind turbine and the series compensation capacitor are obtained as shown in equations (33) and (34), respectively;

[0106]

[0107] Among them, the subscript t represents the quantity at the current moment, the subscript t represents the quantity at the previous moment t-Δt, Δt is the integration step, and i hDFIG(t) Represents the historical current term related to the previous moment; A DFIGd , B DFIGd , C DFIGd , D DFIGd are the coefficient matrices of the discrete state space model of the doubly fed wind turbine, i hDFIG(t-Δt) is the state variable; A cd , B cd , C cd , D cd are the coefficient matrices of the discrete state space model of the series compensation capacitor, i hC(t-Δt)is the state variable;

[0108] According to 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 integration rule, the continuous state space model of the AC transmission line shown in the formula is discretized to obtain its discrete state space model, which is expressed as

[0111]

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

[0113] According to the discrete state space model of AC transmission line in formula (35), the discrete equivalent circuit of two-port element is obtained;

[0114] Further, step S4 is specifically as follows:

[0115] Based on the node analysis method, the discrete state space model of the system is obtained according to the discrete state space model of each component.

[0116] As shown in formula (36);

[0117]

[0118] Among them, the coefficient matrix A d , B d , C d , D d The expressions are

[0119]

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

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

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

[0123] According to the discrete equivalent circuit, the system branch-node association matrix is ​​obtained, as shown in formula (37);

[0124]

[0125] Where I is the identity matrix;

[0126] According to the discrete state space model, the system discrete state space model coefficient matrix D d is the equivalent conductance of each branch element, and the node conductance is expressed as

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

[0128] The branch voltage is expressed by the branch-node connection matrix as

[0129] u (t-Δt) =LU node(t-Δt) (39)

[0130] According to 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 the intermediate variables, the system discrete state matrix is ​​obtained as shown in equation (41);

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

[0134] When the trapezoidal integration rule is used for discretization, the relationship between discrete eigenvalues ​​and continuous eigenvalues ​​is expressed as

[0135]

[0136] Where Δt is the discrete step length, λ i is a continuous eigenvalue, z i is a discrete eigenvalue;

[0137] Therefore, by solving the discrete state matrix A d_sys , the discrete eigenvalue of the system is obtained, and according to the relationship between the discrete eigenvalue and the continuous eigenvalue shown in formula (42), the continuous eigenvalue of the system is obtained.

[0138] The grid-connected characteristic value analysis system of a doubly-fed wind farm considering unbalanced grid voltage adopts the grid-connected characteristic value analysis method of a doubly-fed wind farm considering unbalanced grid voltage as mentioned above to perform grid-connected characteristic value analysis of a doubly-fed wind farm.

[0139] A storage medium having a computer program stored thereon, wherein when the computer program is executed, the above-mentioned method for analyzing grid-connected characteristic values ​​of a doubly-fed wind farm taking into account unbalanced grid voltage is executed.

[0140] Compared with the prior art, the present invention has the following beneficial effects:

[0141] The present invention uses frequency shift transformation to achieve the balance point of the dynamic model of the double-fed wind farm grid-connected system under the condition of unbalanced grid voltage, avoiding the introduction of the double frequency component when using Park transformation to obtain the balance point. A discrete state space model of the double-fed wind turbine grid-connected system is established, simplifying the selection process of the system state variables. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0143] Figure 2 It is a control block diagram of a doubly-fed wind turbine RSC according to a specific embodiment of the present invention;

[0144] Figure 3 A control block diagram of a doubly-fed wind turbine GSC according to a specific embodiment of the present invention;

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

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

[0147] Figure 6 Schematic diagram of a discrete equivalent circuit of a system according to a specific embodiment of the present invention. DETAILED DESCRIPTION

[0148] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention, that is, the embodiments described are only part of the embodiments of the present invention, rather than all of the embodiments. The components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations.

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

[0150] Moreover, the terms "comprises", "includes" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or apparatus that includes a list of elements includes not only those elements, but also includes other elements not explicitly listed, or also includes elements inherent to such process, method, article or apparatus. In the absence of more restrictions, an element defined by the phrase "comprises a ..." does not exclude the presence of additional identical elements in the process, method, article or apparatus that includes the element.

[0151] Example:

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

[0153] The steps include:

[0154] S1.According to Figure 1 The doubly-fed wind turbine is connected to the grid through series compensation. The system components are divided into single-port components and dual-port components according to the connection relationship between the components and the network. In this system, the single-port components include the doubly-fed wind turbine and the series compensation capacitor, and the dual-port components include the transformer and the AC transmission line.

[0155] S2. Establish continuous state space modeling of 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 wind turbine includes a double-mass shaft system equivalent model, a doubly-fed induction motor model, a filter model, and a converter and its control system model. The dynamic mathematical models of each module are as follows:

[0158] 1) Axis model:

[0159]

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

[0161] 2) Generator model

[0162] The motor convention is selected, magnetic saturation and core loss are ignored, and the rotor side winding is converted to the stator side. After conversion, the number of turns of each phase winding is equal. The dynamic mathematical model of the doubly fed induction generator in the three-phase natural static ABC / abc coordinate system is expressed as follows:

[0163] ①Three-phase stator winding voltage equation

[0164]

[0165] Among them, u sA 、u sB 、u sC are the stator ABC three-phase instantaneous voltages, i sA 、i sB 、i sC are the instantaneous currents of the three phases of stator ABC, ψ sA , sB , sC are the stator ABC three-phase winding flux, R s The stator winding voltage is constant.

[0166] The voltage equation of the stator phase A winding is used as an example to illustrate the method of obtaining the equilibrium point based on frequency shift transformation. 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) Represents a complex signal.

[0171] Shift the spectrum of the above complex signal to the left by ω s , and obtain a complex envelope signal whose frequency is concentrated near 0, as shown in formula (5).

[0172]

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

[0174]

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

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

[0177]

[0178] ②Three-phase rotor winding voltage equation

[0179]

[0180] Among them, u ra 、u rb 、u rc are the three-phase instantaneous voltages of the rotor, i ra 、i rb 、i rc are the instantaneous currents of the three phases of rotor ABC, ψ ra , rb , rc They are the rotor ABC three-phase winding flux, R r To set the rotor winding voltage.

[0181] Perform frequency shift transformation on equation (9) to obtain the rotor voltage equation after frequency shift transformation:

[0182]

[0183] ③ Stator and rotor flux equation

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

[0185]

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

[0187] Similarly, frequency shift transformation is performed on equation (13) to 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 expression is as follows:

[0192]

[0193] 3) Controller Model

[0194] Both the rotor side controller (RSC) and the grid side controller (GSC) use vector control based on stator voltage orientation. Unlike the electrical part of the generator, the controller uses a dq synchronous rotating coordinate system, and the input signal is a real signal. Therefore, the controller input signal needs to be further processed. At the same time, due to the three-phase unbalanced grid voltage, the positive and negative sequence controllers of the RSC and GSC need to be designed respectively to suppress the negative sequence component.

[0195] Take any complex signal x i_sfa (i=a,b,c) as an example to illustrate the implementation of the electrical-control signal interface. First, separate the positive and negative sequence signals and obtain

[0196]

[0197] Among them, x1, x2, and x3 represent positive sequence, negative sequence, and zero sequence signals, respectively.

[0198] Furthermore, the positive and negative sequence signals are transformed by Park respectively to obtain the positive and negative sequence signals in the dq coordinate system, which can be expressed as

[0199]

[0200] At this point, the conversion of the complex signal of the electrical part to the real signal of the controller part can be realized. Next, the dynamic mathematical models of RSC and GSC are constructed respectively.

[0201] ①RSC dynamic mathematical model

[0202] according to Figure 2 The RSC control block diagram is shown, and the state equation of RSC is obtained as follows:

[0203]

[0204] according to Figure 2 The control block diagram shown in the figure can be further divided into the algebraic equation as follows:

[0205]

[0206] Since the controller output signal is a real signal, it needs to be converted into a complex signal with the same description form as the electrical part of the generator. The construction method of the complex signal is the same as the construction method of the electrical part complex signal. Therefore, the controller output signal can be further expressed as

[0207]

[0208] Among them, u ar_E 、u br_E 、u cr_E They represent the three-phase rotor voltage after frequency shift, u ar_ERe 、u br_ERe 、u cr_ERe They represent the real part of the rotor phase voltage after frequency shift, u ar_EIm 、u br_EIm 、u cr_EIm They respectively represent the imaginary part of the rotor phase voltage after frequency shift.

[0209] ②GSC dynamic mathematical model

[0210] according to Figure 3 The GSC control block diagram is shown in the figure. The state equation and algebraic equation of GSC can be expressed as

[0211]

[0212]

[0213] ③DC capacitor model

[0214] Ignoring the loss of the converter, according to the law of conservation of energy, the power balance equation of the DC capacitor is:

[0215]

[0216] Among them, C dc is the DC capacitance, u dc is the DC capacitor voltage, P g is the grid-side active power, Pr is the active power on the rotor side.

[0217] 4) Filter model

[0218] The dynamic mathematical model of the filter in the three-phase natural stationary ABC coordinate system is:

[0219]

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

[0221]

[0222] By linearizing equations (1), (15), (19), (22), (23) and (25) at the equilibrium point, the continuous state space model of the doubly fed wind turbine under the condition of grid voltage unbalance is obtained, as shown in equation (26).

[0223]

[0224] Among them, x DFIG =[x M x G x DC x RSC x f x GSC ] T , x M is the axis system state variable, x G is the state variable of the doubly-fed asynchronous motor, x DC is the DC capacitance state variable, x RSC is the rotor side controller state variable, x f is the filter state variable, x GSC is the state variable of the grid-side controller; u DFIG is the input vector, i DFIG is the output vector; A DFIG1 , B DFIG1 , C DFIG1 , D DFIG1 are coefficient matrices respectively.

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

[0226] The dynamic mathematical model of AC line in three-phase natural stationary ABC coordinate system is:

[0227]

[0228] The AC line model after frequency shift conversion can be expressed as

[0229]

[0230] Linearizing equation (28) at the equilibrium point, we obtain the continuous state space model of the AC transmission line, which can be expressed as

[0231]

[0232] Among them, x l is the state variable, u l1 、u l2 is the input vector, i l is the output vector, A l , B l1 ,B l2 ,C l , D l1 , D l2 are coefficient matrices respectively.

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

[0234] The dynamic mathematical model of AC line in three-phase natural stationary ABC coordinate system is:

[0235]

[0236] The AC line model after frequency shift conversion can be expressed as

[0237]

[0238] By linearizing equation (31) at the equilibrium point, we obtain the continuous state space model of the series compensation capacitor, as shown in equation (32).

[0239]

[0240] where x c is the state variable of the series compensation capacitor, u c is the input vector, y c is the output vector, A c1 , B c1 , C c1 , D c1 are coefficient matrices respectively.

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

[0242] According to the connection mode of each component in the doubly fed wind turbine grid-connected system, the system components can be divided into single-port components and dual-port components, among which 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. The discrete state space models of the single-port and dual-port components are established below.

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

[0244] Based on the trapezoidal integration 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, and the discrete state space models of the doubly fed wind turbine and the series compensation capacitor are obtained as shown in equations (33) and (34), respectively.

[0245]

[0246] Among them, the subscript t represents the quantity at the current moment, the subscript t represents the quantity at the previous moment t-Δt, Δt is the integration step, and i hDFIG(t) Represents the historical current term related to the previous moment. A DFIGd , B DFIGd , C DFIGd , D DFIGd are the coefficient matrices of the discrete state space model of the doubly fed wind turbine, i hDFIG(t-Δt) is the state variable. cd , B cd , C cd , D cd are the coefficient matrices of the discrete state space model of the series compensation capacitor, i hC(t-Δt) is a state variable.

[0247] According to 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 shown. Figure 4 in, u mdq and i mdq They represent the node voltage and node current flowing into the element respectively, i hm(t) and G m denote the historical current source and equivalent conductance respectively. The subscript m denotes different one-port components.

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

[0249] Similarly, based on the trapezoidal integration rule, the continuous state space model of the AC transmission line shown in the formula is discretized to obtain its discrete state space model, which is expressed as

[0250]

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

[0252] According to the discrete state space model of AC transmission line in equation (35), the discrete equivalent circuit of two-port element is obtained, as follows: Figure 5 shown. Figure 5 in, u idq and u jdq They represent the node voltages of the two-port element, i idq and i jdq They represent the current flowing into the node of the two-port element, i hn(t) and G n denote the historical current source and equivalent conductance of the two-port element respectively. The subscript n denotes 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 formula (36).

[0254]

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

[0256]

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

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

[0259] according to Figure 6 The discrete equivalent circuit shown in Figure 3 gives the system branch-node association matrix, as shown in equation (37).

[0260]

[0261] Where I is the identity matrix.

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

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

[0264] Furthermore, the branch voltage can be expressed as

[0265] u (t-Δt) =LU node(t-Δt) (39)

[0266] Furthermore, according to 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), eliminating the intermediate variables, we get the system discrete state matrix as shown in equation (41).

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

[0270] When the trapezoidal integration rule is used for discretization, the relationship between discrete eigenvalues ​​and continuous eigenvalues ​​can be expressed as

[0271]

[0272] Where Δt is the discrete step length, λ i is a continuous eigenvalue, z i is a discrete eigenvalue.

[0273] Therefore, by solving the discrete state matrix A d_sys , the discrete eigenvalue of the system can be obtained. Furthermore, according to the relationship between the discrete eigenvalue and the continuous eigenvalue shown in formula (42), the continuous eigenvalue of the system can be obtained.

[0274] The above are preferred embodiments of the present invention. Any changes made according to the technical solution of the present invention, as long as the resulting functions do not exceed the scope of the technical solution of the present invention, belong to the protection scope of the present invention.

Claims

1. A method for analyzing the grid-connected characteristic values ​​of a doubly-fed wind farm considering unbalanced grid voltage, characterized in that: The following steps are involved: S1: Based on the topological structure of the grid-connected doubly-fed wind farm system, a dynamic mathematical model of each component is established; S2: Obtain the system equilibrium point based on frequency shift transformation, linearize the system model at the equilibrium point, and establish a linearized continuous state space model; S3: According to 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 dual-port components. The continuous state space model of each component is discretized using the ladder integration rule, and the 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 node method is used to construct the discrete state space model of the whole system; S5: Obtain a discrete state matrix, obtain continuous eigenvalues ​​based on the relationship between discrete eigenvalues ​​and continuous eigenvalues, and perform eigenvalue analysis.

2. The method for analyzing the grid-connected characteristic values ​​of a doubly-fed wind farm considering unbalanced grid voltage according to claim 1, characterized in that: Step S1 is specifically as follows: According to the structure of the doubly fed wind turbine connected to the grid through series compensation, the system components are divided into single-port components and dual-port components according to the connection relationship between the components and the network. In the system, the single-port components include the doubly fed wind turbine and the series compensation capacitor, and the dual-port components include the transformer and the AC transmission line.

3. The method for analyzing the grid-connected characteristic values ​​of a doubly-fed wind farm considering unbalanced grid voltage according to claim 2, characterized in that: Step S2 is specifically as follows: The continuous state space modeling of single-port and dual-port components in the dq synchronous rotating coordinate system is established respectively; (1) Continuous state space modeling of doubly-fed wind turbine; The dynamic mathematical model of the doubly-fed wind turbine includes a double-mass shaft system equivalent model, a doubly-fed induction motor model, a filter model, and a converter and its control system model. The dynamic mathematical models of each module are as follows: 1) Axis model: Among them, H t is the fan inertia constant, H g is the generator rotor inertia constant, ω t is the fan shaft speed, ω r Rotor speed, T m is the mechanical torque of the fan, T e is the electromagnetic torque of the fan, K s is the shaft stiffness coefficient, θ s is the angular displacement of the shaft system, θ r is the rotor angular displacement, B s is the shaft damping coefficient; 2) Generator model: The motor convention is selected, magnetic saturation and core loss are ignored, and the rotor side winding is converted to the stator side. After conversion, the number of turns of each phase winding is equal; the dynamic mathematical model of the doubly fed induction generator in the three-phase natural stationary ABC / abc coordinate system is expressed as follows: ①Three-phase stator winding voltage equation Among them, u sA 、u sB 、u sC are the stator ABC three-phase instantaneous voltages, i sA 、i sB 、i sC are the instantaneous currents of the three phases of stator ABC, ψ sA , sB , sC are the stator ABC three-phase winding flux, R s To set the voltage for stator winding; Taking the stator A phase winding voltage equation as an example, the method of obtaining the equilibrium point based on frequency shift transformation is explained; first, the imaginary part of the signal is constructed, as shown in formula (3); The voltage equation is expressed in complex form, as shown in equation (4): In the formula, ψ sA-s(t) represents a complex signal; Shift the spectrum of the above complex signal to the left by ω s , we get a complex envelope signal whose frequency is concentrated around 0, as shown in formula (5); Separate the real and imaginary parts of the above equation and express it as Wherein, subscript E represents the signal after frequency shift transformation, subscript Re represents the real part of the complex signal, and subscript Im represents the imaginary part of the complex signal; Similarly, the equation after BC phase-frequency shift transformation can be obtained, which is expressed as ②Three-phase rotor winding voltage equation Among them, u ra 、u rb 、u rc are the three-phase instantaneous voltages of the rotor, i ra 、i rb 、i rc are the three-phase instantaneous currents of the rotor ABC, ra , rb , rc They are the rotor ABC three-phase winding flux, R r To set the voltage for the rotor winding; Perform frequency shift transformation on equation (9) to obtain the rotor voltage equation after frequency shift transformation: ③ Stator and rotor flux equation The stator and rotor flux equations in the three-phase natural stationary ABC / abc coordinate system are expressed as Where ψ s =[ψ sA ,ψ sB ,ψ sC ],ψ r =[ψ ra ,ψ rb ,ψ rc ], L ss is the inductance matrix between stator windings, L rr is the inductance matrix between the rotor windings, L sr and L rs is the mutual inductance matrix between the stator winding and the rotor winding, and L sr =L rs T ; Similarly, frequency shift transformation is performed on equation (13) to obtain 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: The coefficient matrix expression is as follows: 3) Controller Model: Both the rotor-side controller and the grid-side controller adopt vector control based on stator voltage orientation. The controller adopts dq synchronous rotating coordinate system, and the input signal is a real signal. Therefore, the controller input signal needs to be further processed. At the same time, the positive and negative sequence controllers of RSC and GSC are designed respectively to suppress the negative sequence component. Take any complex signal x i_sfa Take for example, i = a, b, c, to illustrate the implementation of the electrical-control signal interface; First, the positive and negative sequence signals are separated, and according to the symmetrical component method, we get Among them, x1, x2, and x3 represent positive sequence, negative sequence, and zero sequence signals, respectively. Perform Park transform on the positive and negative sequence signals respectively to obtain the positive and negative sequence signals in the dq coordinate system, which are expressed as At this point, the conversion of the complex signal of the electrical part to the real signal of the controller part can be realized; next, the dynamic mathematical models of RSC and GSC are constructed respectively; ①RSC dynamic mathematical model: The state equation of RSC is The algebraic equation is Convert it into a complex signal with the same description form as the electrical part of the generator; the construction method of the complex signal is the same as the construction method of the electrical part complex signal; therefore, the controller output signal is expressed as Among them, u ar_E 、u br_E 、u cr_E They represent the three-phase rotor voltage after frequency shift, u ar_ERe 、u br_ERe 、u cr_ERe They represent the real part of the rotor phase voltage after frequency shift, u ar_EIm 、u br_EIm 、u cr_EIm They represent the imaginary part of the rotor phase voltage after frequency shifting respectively; ②GSC dynamic mathematical model: The state equation and algebraic equation of GSC are expressed as ③DC capacitor model: According to the law of conservation of energy, the power balance equation of DC capacitor is: Among them, C dc is the DC capacitance, u dc is the DC capacitor voltage, P g is the grid-side active power, P r is the active power on the rotor side; 4) Filter model: The dynamic mathematical model of the filter in the three-phase natural stationary ABC coordinate system is: The filter model after frequency shift transformation is expressed as By linearizing equations (1), (15), (19), (22), (23) and (25) at the equilibrium point, the continuous state space model of the doubly fed wind turbine under the condition of grid voltage unbalance is obtained, as shown in equation (26); Among them, x DFIG =[x M x G x DC x RSC x f x GSC ] T , x M is the axis system state variable, x G is the state variable of the doubly-fed asynchronous motor, x DC is the DC capacitance state variable, x RSC is the rotor side controller state variable, x f is the filter state variable, x GSC is the state variable of the grid-side controller; u DFIG is the input vector, i DFIG is the output vector; A DFIG1 , B DFIG1 , C DFIG1 , D DFIG1 are coefficient matrices respectively; (2) Continuous state space modeling of transmission lines: The dynamic mathematical model of AC line in three-phase natural stationary ABC coordinate system is: The AC line model after frequency shift conversion is expressed as Linearizing equation (28) at the equilibrium point, we obtain the continuous state space model of the AC transmission line, which is expressed as Among them, x l is the state variable, u l1 、u l2 is the input vector, i l is the output vector, A l , B l1 ,B l2 ,C l , D l1 , D l2 are coefficient matrices respectively; (3) Continuous state space modeling of series compensation capacitor: The dynamic mathematical model of AC line in three-phase natural stationary ABC coordinate system is: The AC line model after frequency shift conversion is expressed as Linearize equation (31) at the equilibrium point to obtain the continuous state space model of the series compensation capacitor, as shown in equation (32); where x c is the state variable of the series compensation capacitor, u c is the input vector, y c is the output vector, A c1 , B c1 , C c1 , D c1 are coefficient matrices respectively.

4. The method for analyzing the grid-connected characteristic values ​​of a doubly-fed wind farm considering unbalanced grid voltage according to claim 3 is characterized in that: Step S3 is as follows: According to the connection mode of each component in the doubly-fed wind turbine grid-connected system, the system components are divided into single-port components and double-port components, among which the single-port components are the doubly-fed wind turbine and the series compensation capacitor, and the double-port components are the AC transmission line. The discrete state space models of single / dual port components are established below; (1) Discrete state space modeling of single-port elements: Based on the trapezoidal integration 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, and the discrete state space models of the doubly fed wind turbine and the series compensation capacitor are obtained as shown in equations (33) and (34), respectively; Among them, the subscript t represents the quantity at the current moment, the subscript t represents the quantity at the previous moment t-Δt, Δt is the integration step, and i hDFIG(t) Represents the historical current term related to the previous moment; A DFIGd , B DFIGd , C DFIGd , D DFIGd are the coefficient matrices of the discrete state space model of the doubly fed wind turbine, i hDFIG(t-Δt) is the state variable; A cd , B cd , C cd , D cd are the coefficient matrices of the discrete state space model of the series compensation capacitor, i hC(t-Δt) is the state variable; According to the discrete state space model of the single-port element shown in equations (33) and (34), its discrete equivalent circuit is obtained; (2) Discrete state space modeling of two-port components: Similarly, based on the trapezoidal integration rule, the continuous state space model of the AC transmission line shown in the formula is discretized to obtain its discrete state space model, which is expressed as Among them, A ld , B ld , C ld , D ld are the coefficient matrices of the discrete state space model of the AC transmission line, i hl(t-Δt) is the state variable; According to the discrete state space model of the AC transmission line in equation (35), the discrete equivalent circuit of the two-port element is obtained.

5. The method for analyzing the grid-connected characteristic values ​​of a doubly-fed wind farm considering unbalanced grid voltage according to claim 4, characterized in that: Step S4 is specifically as follows: Based on the node analysis method, the discrete state space model of the system is obtained according to the discrete state space model of each component, as shown in formula (36); Among them, the coefficient matrix A d , B d , C d , D d The expressions are The discrete equivalent circuit of the doubly-fed wind farm grid-connected system is obtained.

6. The method for analyzing the grid-connected characteristic values ​​of a doubly-fed wind farm considering unbalanced grid voltage according to claim 5, characterized in that: Step S5 is specifically as follows: Based on the system discrete state empty model, the system discrete state matrix is ​​obtained; the calculation method is as follows: According to the discrete equivalent circuit, the system branch-node association matrix is ​​obtained, as shown in formula (37); Where I is the identity matrix; According to the discrete state space model, the system discrete state space model coefficient matrix D d is the equivalent conductance of each branch element, and the node conductance is expressed as G=L T D d L (34) The branch voltage is expressed by the branch-node connection matrix as u (t-Δt) =LU node(t-Δt) (39) According to the relationship between node voltage and node current, the node voltage is expressed as U node(t-Δt) =G -1 L T C d i h(t-Δt) (40) Combining equations (12)-(15), eliminating the intermediate variables, the system discrete state matrix is ​​obtained as shown in equation (41); And d_sys =A d +B d LG -1 L T C d (41) When the trapezoidal integration rule is used for discretization, the relationship between discrete eigenvalues ​​and continuous eigenvalues ​​is expressed as Where Δt is the discrete step length, λ i is a continuous eigenvalue, z i is a discrete eigenvalue; Therefore, by solving the discrete state matrix A d_sys , the discrete eigenvalue of the system is obtained, and according to the relationship between the discrete eigenvalue and the continuous eigenvalue shown in formula (42), the continuous eigenvalue of the system is obtained.

7. A doubly-fed wind farm grid-connected characteristic value analysis system considering unbalanced grid voltage, characterized in that: The grid-connected characteristic value analysis method of a doubly-fed wind farm considering unbalanced grid voltage as described in any one of claims 1 to 6 is used to perform grid-connected characteristic value analysis of a doubly-fed wind farm.

8. A storage medium, characterized in that: The storage medium stores a computer program, which, when executed, executes the method for analyzing grid-connected characteristic values ​​of a doubly-fed wind farm considering unbalanced grid voltage as described in any one of claims 1 to 6.

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